How many questions from Geometrical Optics appear in JEE?

Geometrical Optics has appeared in 172 of the last 186 JEE Main and JEE Advanced papers — about 92% of them — contributing 259 questions in total across those papers.

Is Geometrical Optics an important chapter for JEE?

Judged by how often it is actually tested, it appears in roughly 92% of papers. Chapters above about 50% are effectively guaranteed to show up every session, so they repay thorough preparation; lower-frequency chapters are better treated as targeted revision.

Where do these Geometrical Optics questions come from?

Every question is from an official JEE Main or JEE Advanced paper, transcribed from the original paper and tagged to this chapter. Answers follow the official answer key.

Geometrical Optics JEE Previous Year Questions with Answers

Q1·PhysicsSingle correctJEE Advanced 2026

A beam of polychromatic light passes through a thin prism of prism angle 6°. The refractive index of the material of the prism varies with wavelength

(\lambda)

as

n(\lambda) = \alpha\lambda + \frac{\beta}{\lambda^{2}}

, where

\alpha = 3\ \mu\mathrm{m}^{-1}

and

\beta = 0.096\ \mu\mathrm{m}^{2}

. If

\lambda_{\min}

is the wavelength at which the angle of minimum deviation

D_{m}

is smallest, then the correct value of

D_{m}

at

\lambda_{\min}

is

(A)6.4°
(B)4.8°
(C)3.2°
(D)2.4°

Q2·PhysicsMultiple correctJEE Advanced 2026

Consider two isosceles prisms 1 and 2 with prism angles

A_{1}

and

A_{2}

and refractive indices

n_{1}

and

n_{2}

, respectively, as shown in the figure. The faces

a_{1}b_{1}

and

a_{2}b_{2}

are parallel to each other and perpendicular to the mirror

M

. If a ray of light is incident on the face

a_{1}c_{1}

and emerges from the face

a_{2}c_{2}

, then the correct statement(s) is/are:

(A)If both the prisms are at minimum deviation condition, then $\frac{n_{2}}{n_{1}} = \sin\left(\frac{A_{1}}{2}\right) / \sin\left(\frac{A_{2}}{2}\right)$ .
(B)If prism 2 is at minimum deviation condition, then $\sin i_{1} = n_{2}\sin\left(\frac{A_{2}}{2}\right)$ is always true.
(C)If both the prisms 1 and 2 are thin and are at minimum deviation condition with angles of deviation $\delta_{m1}$ and $\delta_{m2}$ , respectively, then $\theta = \frac{\delta_{m1}}{2(n_{1} - 1)} + \frac{\delta_{m2}}{2(n_{2} - 1)}$ .
(D)If prism 1 is at minimum deviation condition, then $\sin i_{2} = n_{1}\sin\left(\frac{A_{1}}{2}\right)$ is always true.

Q3·PhysicsSingle correctJEE Advanced 2026

A double convex lens made of glass of refractive index 1.5 and radii of curvature of the curved surfaces 20 cm each is immersed in a liquid of refractive index

n_L

. The correct plot showing the variation of the power, in the units of diopter

(D)

, as a function of

n_L

is:

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q4·PhysicsSingle correctJEE Main 2026

A thin biconvex lens is prepared from the glass

(\mu = 1.5)

both curved surfaces of which have equal radii of 20 cm each. Left side surface of the lens is silvered from outside to make it reflecting. To have the position of image and object at the same place, the object should be placed, from the lens at a distance of ________ cm.

(A)10
(B)12.5
(C)13
(D)13.5

Q5·PhysicsSingle correctJEE Main 2026

Light ray incident along a vector

\vec{AO}

(

\vec{AO} = 2\hat{i} - 3\hat{j}

) emerges out along vector

\vec{OB}

(

\vec{OB} = C\hat{i} - 4\hat{j}

) as shown in the figure below. The value of

C

is ________.

(A)1.6
(B)0.16
(C)11.6
(D)16

Q6·PhysicsNumericalJEE Main 2026

A concave mirror of focal length 10 cm forms an image which is double the size of object when the object is placed at two different positions. The distance between the two positions of the object is __________ cm.

Q7·PhysicsSingle correctJEE Main 2026

Angle of minimum deviation is equal to the half of the angle of prism in an equilateral prism. The refractive index of the prism is __________.

(A)1.5
(B) $\sqrt{3}$
(C) $\sqrt{2}$
(D)1.65

Q8·PhysicsSingle correctJEE Main 2026

A spherical interface lens of radius

R

separates two media of refractive indices 1 and 1.4 respectively as shown in the figure below. A point source is placed at a distance of

4R

in front of spherical interface. The magnitude of the magnification of point source image is _______.

(A)1.66
(B)2.33
(C)2.66
(D)1.33

Q9·PhysicsSingle correctJEE Main 2026

A thin convex lens and a thin concave lens are kept in contact and are co-axial. Which of the following statements is correct for this combination of two lenses ?

(A)behaves as concave lens if $|f_\mathrm{convex}| > |f_\mathrm{concave}|$
(B)behaves as concave lens if $|f_\mathrm{convex}| < |f_\mathrm{concave}|$
(C)behaves as convex lens if $|f_\mathrm{convex}| > |f_\mathrm{concave}|$
(D)Focal length of the lens system will change if the positions of two lenses are interchanged

Q10·PhysicsSingle correctJEE Main 2026

An object

AB

is placed 15 cm on the left of a convex lens

P

of focal length 10 cm. Another convex lens

Q

is now placed 15 cm right of lens

P

. If the focal length of lens

Q

is 15 cm, the final image is ________.

(A)virtual, formed at 7.5 cm right of lens $Q$ , with a size bigger than that of $AB$
(B)real, formed at 7.5 cm right of lens $Q$ , with a size same as that of $AB$
(C)formed at infinity.
(D)real, formed at 7 cm right of lens $Q$ , with a size smaller than that of $AB$

Q11·PhysicsSingle correctJEE Main 2026

A ray of light passing through an equilateral prism is having velocity

2.12 \times 10^{8}

m/s in the prism material, then the minimum angle of deviation is _____ degrees.

(A)45
(B)30
(C)28
(D)58

Q12·PhysicsSingle correctJEE Main 2026

A compound microscope is designed with two symmetric biconvex lenses. The objective lens is cut vertically, creating two identical plano-convex lenses. One of them is used in place of original objective lens. To retain same magnification keeping the object distance unchanged, the tube length has to be

(A)increased two times
(B)increased $\frac{3}{2}$ times
(C)decreased two times
(D)decreased $\frac{3}{2}$ times

Q13·PhysicsSingle correctJEE Main 2026

A convex lens is made from glass material having refractive index of 1.4 with same radius of curvature on both sides. The ratio of its focal length and radius of curvature is ______.

(A)0.5
(B)2.5
(C)0.8
(D)1.25

Q14·PhysicsSingle correctJEE Main 2026

A rod of length 10 cm lies along the principle axis of a concave mirror of focal length 10 cm as shown in figure. The length of the image is ______ cm.

(A)2.5
(B)5
(C)7.5
(D)7

Q15·PhysicsNumericalJEE Main 2026

If sunlight is focused on a paper using convex lens, it starts burning the paper in shortest time when the lens is kept at 30 cm above the paper. If the radius of curvature of the lens is 60 cm then the refractive index of the lens material is

\frac{\alpha}{10}

. The value of

\alpha

is ________.

Q16·PhysicsSingle correctJEE Main 2026

Refer the figure given below.

\mu_{1}

and

\mu_{2}

are refractive indices of air and lens material. The height of image will be ________ cm.

(A)1
(B)0.5
(C)1.2
(D)0.25

Q17·PhysicsSingle correctJEE Main 2026

One side of an equilateral prism is painted by a transparent material of refractive index

n_2

. The refractive index of prism is 1.6. The minimum value of

n_2

required for total internal reflection from painted face is ________.

(A) $3\sqrt{3}/1.6$
(B) $\sqrt{3}$
(C) $3.2/\sqrt{3}$
(D) $4\sqrt{3}/5$

Q18·PhysicsSingle correctJEE Main 2026

For a thin symmetric prism made of glass (refractive index 1.5), the ratio of incident angle and minimum deviation will be ________.

(A)3 : 4
(B)3 : 2
(C)2 : 1
(D)1 : 2

Q19·PhysicsSingle correctJEE Main 2026

A biconvex lens is formed by using two thin planoconvex lenses, as shown in the figure. The refractive index and radius of curved surfaces are also mentioned in figure. When an object is placed on the left side of lens at a distance of 30 cm from the biconvex lens, the magnification of the image will be :

(A)–2
(B)+2
(C)+2.5
(D)–2.5

Q20·PhysicsSingle correctJEE Main 2026

For a transparent prism, if the angle of minimum deviation is equal to its refracting angle, the refractive index n of the prism satisfies.

(A) $\sqrt{2} < n < 2\sqrt{2}$
(B) $1 < n < 2$
(C) $n \geq 2$
(D) $\sqrt{2} < n < 2$

Q21·PhysicsSingle correctJEE Main 2026

The magnitudes of power of a biconvex lens (refractive index 1.5) and that of a plano-concave lens (refractive index = 1.7) are same. If the curvature of plano-concave lens exactly matches with the curvature of back surface of the biconvex lens, then ratio of radius of curvature of front and back surface of the biconvex lens is ________ .

(A)5 : 2
(B)5 : 12
(C)12 : 5
(D)2 : 5

Q22·PhysicsNumericalJEE Main 2026

A convex lens of refractive index 1.5 and focal length

f

= 18 cm is immersed in water. The difference in focal lengths of the given lens when it is in water and in air is α × f . The value of α is _________. (refractive index of water = 4/3)

Q23·PhysicsSingle correctJEE Main 2026

In a microscope of tube length 10 cm two convex lenses are arranged with focal length of 2 cm and 5 cm. Total magnification obtained with this system for normal adjustment is

(5)^{k}

. The value of k is_____

(A)2
(B)5
(C)3.5
(D)4

Q24·PhysicsSingle correctJEE Main 2026

Distance between an object and three times magnified real image is 40 cm. The focal length of the mirror used is _____ cm.

(A) $-15/2$
(B) $-10$
(C) $-20$
(D) $-15$

Q25·PhysicsSingle correctJEE Main 2026

Five persons

P_1

,

P_2

,

P_3

,

P_4

and

P_5

recorded object distance (u) and image distance (v) using same convex lens having power

+5D

as (25,96), (30,62), (35,37), (45,35) and (50,32) respectively. Identify correct statement

(A)Readings recorded by all persons are correct
(B)Reading recorded by $P_3$ persons are incorrect
(C)Reading recorded by $P_3$ and $P_2$ persons are incorrect
(D)Reading recorded by $P_4$ and $P_5$ persons are incorrect

Q26·PhysicsSingle correctJEE Main 2026

The exit surface of a prism with refractive index n is coated with a material having refractive index

\dfrac{n}{2}

. When this prism is set for minimum angle of deviation it exactly meets the condition of critical angle. The prism angle is____

(A)60°
(B)15°
(C)30°
(D)45°

Q27·PhysicsSingle correctJEE Main 2026

A thin prism with angle 5° of refractive index 1.72 is combined with another prism of refractive index 1.9 to produce dispersion without deviation. The angle of second prism is _______.

(A)4.5°
(B)6°
(C)4°
(D)5°

Q28·PhysicsNumericalJEE Main 2026

The size of the images of an object, formed by a thin lens are equal when the object is placed at two different positions 8 cm and 24 cm from the lens. The focal length of the lens is ________ cm.

Q29·PhysicsSingle correctJEE Main 2026

Consider light travelling from a medium A to medium B separated by a plane interface. If the light undergoes total internal reflection during its travel from medium A to B and the speed of light in media A and B are

2.4 \times 10^8

m/s and

2.7 \times 10^8

m/s respectively, then the value of critical angle is :

(A) $\cot^{-1}\left(\frac{3}{\sqrt{13}}\right)$
(B) $\sin^{-1}\left(\frac{9}{8}\right)$
(C) $\tan^{-1}\left(\frac{8}{\sqrt{17}}\right)$
(D) $\cos^{-1}\left(\frac{8}{9}\right)$

Q30·PhysicsNumericalJEE Main 2026

A parallel beam of light travelling in air (refractive index 1.0) is incident on a convex spherical glass surface of radius of curvature 50 cm. Refractive index of glass is 1.5. The rays converge to a point at a distance x cm from the centre of the curvature of the spherical surface. The value of x is ____ cm.

Q31·PhysicsSingle correctJEE Main 2026

Consider an equilateral prism (refractive index

\sqrt{2}

). A ray of light is incident on its one surface at a certain angle

i

. If the emergent ray is found to graze along the other surface then the angle of refraction at the incident surface is close to ____.

(A)15°
(B)20°
(C)40°
(D)30°

Q32·PhysicsSingle correctJEE Main 2026

As shown in the diagram, when the incident ray is parallel to base of the prism, the emergent ray grazes along the second surface. If refractive index of the material of prism is

\sqrt{2}

, the angle

\theta

of prism is.

(A)60°
(B)75°
(C)90°
(D)45°

Q33·PhysicsNumericalJEE Main 2026

In a microscope the objective is having focal length

f_0

= 2 cm and eye-piece is having focal length

f_e

= 4 cm. The tube length is 32 cm. The magnification produced by this microscope for normal adjustment is ___________.

Q34·PhysicsNumericalJEE Main 2026

A collimated beam of light of diameter 2 mm is propagating along x-axis. The beam is required to be expanded in a collimated beam of diameter 14 mm using a system of two convex lenses. If first lens has focal length 40 mm, then the focal length of second lens is ________ mm.

Q35·PhysicsMultiple correctJEE Advanced 2025

Two identical concave mirrors each of focal length f are facing each other as shown in the schematic diagram. The focal length f is much larger than the size of the mirrors. A glass slab of thickness t and refractive index

n_0

is kept equidistant from the mirrors and perpendicular to their common principal axis. A monochromatic point light source S is embedded at the center of the slab on the principal axis, as shown in the schematic diagram. For the image to be formed on S itself, which of the following distances between the two mirrors is/are correct:

(A) $4f + \left(1 - \frac{1}{n_0}\right)t$
(B) $2f + \left(1 - \frac{1}{n_0}\right)t$
(C) $4f + (n_0 - 1)t$
(D) $2f + (n_0 - 1)t$

Q36·PhysicsNumericalJEE Advanced 2025

A solid glass sphere of refractive index

n = \sqrt{3}

and radius R contains a spherical air cavity of radius

\frac{R}{2}

, as shown in the figure. A very thin glass layer is present at the point O so that the air cavity (refractive index n = 1) remains inside the glass sphere. An unpolarized, unidirectional and monochromatic light source S emits a light ray from a point inside the glass sphere towards the periphery of the glass sphere. If the light is reflected from the point O and is fully polarized, then the angle of incidence at the inner surface of the glass sphere is θ. The value of sin θ is ______

Q37·PhysicsSingle correctJEE Main 2025

A concave-convex lens of refractive index 1.5 and the radii of curvature of its surfaces are 30 cm and 20 cm, respectively. The concave surface is upwards and is filled with a liquid of refractive index 1.3. The focal length of the liquid-glass combination will be:

(A) $\dfrac{500}{11}$ cm
(B) $\dfrac{800}{11}$ cm
(C) $\dfrac{700}{11}$ cm
(D) $\dfrac{600}{11}$ cm

Q38·PhysicsSingle correctJEE Main 2025

A convex lens of focal length 30 cm is placed in contact with a concave lens of focal length 20 cm. An object is placed at 20 cm to the left of this lens system. The distance of the image from the lens in cm is ___

(A) $30$
(B) $45$
(C) $\dfrac{60}{7}$
(D) $15$

Q39·PhysicsIntegerJEE Main 2025

A container contains a liquid with refractive index 1.2 up to a height of 60 cm and another liquid having refractive index 1.6 is added to height H above first liquid. If viewed from above, the apparent shift in the position of bottom of container is 40 cm. The value of H is ______ cm. (Consider liquids are immiscible)

Q40·PhysicsSingle correctJEE Main 2025

Two thin convex lenses of focal lengths 30 cm and 10 cm are placed coaxially, 10 cm apart. The power of this combination is:

(A)5 D
(B)1 D
(C)20 D
(D)10 D

Q41·PhysicsSingle correctJEE Main 2025

A lens having refractive index 1.6 has focal length of 12 cm, when it is in air. Find the focal length of the lens when it is placed in water. (Take refractive index of water as 1.28)

(A)355 mm
(B)288 mm
(C)555 mm
(D)655 mm

Q42·PhysicsSingle correctJEE Main 2025

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Refractive index of glass is higher than that of air. Reason (R): Optical density of a medium is directly proportionate to its mass density which results in a proportionate refractive index. In the light of the above statements, choose the most appropriate answer from the options given below:

(A)(A) is not correct but (R) is correct
(B)Both (A) and (R) are correct and (R) is the correct explanation of (A)
(C)(A) is correct but (R) is not correct
(D)Both (A) and (R) are correct but (R) is not the correct explanation of (A)

Q43·PhysicsSingle correctJEE Main 2025

A mirror is used to produce an image with magnification of

\dfrac{1}{4}

. If the distance between object and its image is 40 cm, then the focal length of the mirror is __________.

(A)10 cm
(B)12.7 cm
(C)10.7 cm
(D)15 cm

Q44·PhysicsSingle correctJEE Main 2025

A transparent block A having refractive index

\mu=1.25

is surrounded by another medium of refractive index

\mu=1.0

as shown in the figure. A light ray is incident on the flat face of the block with incident angle

\theta

as shown in the figure. What is the maximum value of

\theta

for which light suffers total internal reflection at the top surface of the block?

(A) $\tan^{-1}(4/3)$
(B) $\tan^{-1}(3/4)$
(C) $\sin^{-1}(3/4)$
(D) $\cos^{-1}(3/4)$

Q45·PhysicsIntegerJEE Main 2025

Distance between object and its image (magnified by

-\dfrac{1}{3}

) is 30 cm. The focal length of the mirror used is

\left(\dfrac{x}{4}\right)

cm, where magnitude of value of

x

is ______.

Q46·PhysicsSingle correctJEE Main 2025

When an object is placed 40 cm away from a spherical mirror an image of magnification

\dfrac{1}{2}

is produced. To obtain an image with magnification of

\dfrac{1}{3}

, the object is to be moved:

(A)40 cm away from the mirror.
(B)80 cm away from the mirror.
(C)20 cm towards the mirror.
(D)20 cm away from the mirror.

Q47·PhysicsSingle correctJEE Main 2025

A finite size object is placed normal to the principal axis at a distance of 30 cm from a convex mirror of focal length 30 cm. A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is:

(A)45 cm
(B)7.5 cm
(C)22.5 cm
(D)15 cm

Q48·PhysicsIntegerJEE Main 2025

Light from a point source in air falls on a spherical glass surface (refractive index

\mu=1.5

and radius of curvature

=50

cm). The image is formed at a distance of 200 cm from the glass surface inside the glass. The magnitude of distance of the light source from the glass surface is __________ m.

Q49·PhysicsSingle correctJEE Main 2025

The radii of curvature for a thin convex lens are 10 cm and 15 cm respectively. The focal length of the lens is 12 cm. The refractive index of the lens material is:

(A)1.2
(B)1.4
(C)1.5
(D)1.8

Q50·PhysicsSingle correctJEE Main 2025

A monochromatic light of frequency

5\times10^{14}

Hz travelling through air, is incident on a medium of refractive index '2'. Wavelength of the refracted light will be:

(A)300 nm
(B)600 nm
(C)400 nm
(D)500 nm

Q51·PhysicsSingle correctJEE Main 2025

Consider the following statements for refraction of light through a prism, when the angle of deviation is minimum. (A) The refracted ray inside the prism becomes parallel to the base. (B) Larger angle prisms provide smaller angle of minimum deviation. (C) Angle of incidence and angle of emergence become equal. (D) There are always two sets of angle of incidence for which deviation will be same except at the minimum deviation setting. (E) Angle of refraction becomes double of the prism angle. Choose the correct answer from the options given below:

(A)(A), (C) and (D) Only
(B)(B), (C) and (D) Only
(C)(A), (B) and (E) Only
(D)(B), (D) and (E) Only

Q52·PhysicsSingle correctJEE Main 2025

A spherical surface separates two media of refractive indices 1 and 1.5 as shown in the figure. Distance of the image of an object ‘O’, is: (

C

is the centre of curvature of the spherical surface and

R

is the radius of curvature)

(A)0.24 m right to the spherical surface
(B)0.4 m left to the spherical surface
(C)0.24 m left to the spherical surface
(D)0.4 m right to the spherical surface

Q53·PhysicsSingle correctJEE Main 2025

A bi-convex lens has radius of curvature of both the surfaces same as

1/6

cm. If this lens is required to be replaced by another convex lens having different radii of curvatures on both sides

(R_1\ne R_2)

, without any change in lens power, then the possible combination of

R_1

and

R_2

is:

(A) $\dfrac{1}{3}$ cm and $\dfrac{1}{3}$ cm
(B) $\dfrac{1}{5}$ cm and $\dfrac{1}{7}$ cm
(C) $\dfrac{1}{3}$ cm and $\dfrac{1}{7}$ cm
(D) $\dfrac{1}{6}$ cm and $\dfrac{1}{9}$ cm

Q54·PhysicsSingle correctJEE Main 2025

A slanted object AB is placed on one side of a convex lens as shown in the diagram. The image is formed on the opposite side. Angle made by the image with the principal axis is:

(A) $-\dfrac{\alpha}{2}$
(B) $-45^\circ$
(C) $+45^\circ$
(D) $-\alpha$

Q55·PhysicsIntegerJEE Main 2025

A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to

60^\circ

. The refractive index of the prism material is

\sqrt2

. The angle of incidence (in degrees) is ______.

Q56·PhysicsSingle correctJEE Main 2025

Two identical objects are placed in front of a convex mirror and a concave mirror having same radii of curvature of 12 cm, at same distance of 18 cm from the respective mirrors. The ratio of sizes of the images formed by the convex mirror and by the concave mirror is:

(A) $1/2$
(B) $2$
(C) $3$
(D) $1/3$

Q57·PhysicsSingle correctJEE Main 2025

Two concave refracting surfaces of equal radii of curvature and refractive index 1.5 face each other in air as shown in figure. A point object O is placed midway, between P and B. The separation between the images of O, formed by each refracting surface is:

(A)0.214R
(B)0.114R
(C)0.411R
(D)0.124R

Q58·PhysicsSingle correctJEE Main 2025

A convex lens made of glass (refractive index = 1.5) has focal length 24 cm in air. When it is totally immersed in water (refractive index = 1.33), its focal length changes to

(A)72 cm
(B)96 cm
(C)24 cm
(D)48 cm

Q59·PhysicsSingle correctJEE Main 2025

Let u and v be the distances of the object and the image from a lens of focal length f. The correct graphical representation of u and v for a convex lens when

|u|>f

, is (see figure):

(A)(1)
(B)(2)
(C)(3)
(D)(4)

Q60·PhysicsSingle correctJEE Main 2025

Two identical symmetric double convex lenses of focal length f are cut into two equal parts

L_1, L_2

by AB plane and

L_3, L_4

by XY plane as shown in figure. The ratio of focal lengths of lenses

L_1

and

L_3

is

(A)1 : 4
(B)1 : 1
(C)2 : 1
(D)1 : 2

Q61·PhysicsIntegerJEE Main 2025

Two light beams fall on a transparent material block at point 1 and 2 with angle

\theta_1

and

\theta_2

, respectively, as shown in figure. After refraction, the beams intersect at point 3 which is exactly on the interface at other end of the block. Given: the distance between 1 and 2,

d=4\sqrt{3}

cm and

\theta_1=\theta_2=\cos^{-1}\left(\dfrac{n_2}{2n_1}\right)

, where refractive index of the block

n_2

> refractive index of the outside medium

n_1

, then the thickness of the block is ______ cm.

Q62·PhysicsSingle correctJEE Main 2025

In a long glass tube, mixture of two liquids A and B with refractive indices 1.3 and 1.4 respectively, forms a convex refractive meniscus towards A. If an object placed at 13 cm from the vertex of the meniscus in A forms an image with a magnification of '-2' then the radius of curvature of meniscus is:

(A)1 cm
(B) $\frac{1}{3}$ cm
(C) $\frac{2}{3}$ cm
(D) $\frac{4}{3}$ cm

Q63·PhysicsSingle correctJEE Main 2025

A concave mirror produces an image of an object such that the distance between the object and image is 20 cm. If the magnification of the image is '-3', then the magnitude of the radius of curvature of the mirror is:

(A)3.75 cm
(B)30 cm
(C)7.5 cm
(D)15 cm

Q64·PhysicsSingle correctJEE Main 2025

A thin prism

P_1

with angle

4^\circ

made of glass having refractive index 1.54, is combined with another thin prism

P_2

made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism

P_2

in degrees is

(A)4
(B)3
(C) $\frac{16}{3}$
(D)1.5

Q65·PhysicsIntegerJEE Main 2025

A thin transparent film with refractive index 1.4, is held on circular ring of radius 1.8 cm. The fluid in the film evaporates such that transmission through the film at wavelength 560 nm goes to a minimum every 12 seconds. Assuming that the film is flat on its two sides, the rate of evaporation is ______

\pi\times10^{-13}

m

^3

/s.

Q66·PhysicsSingle correctJEE Main 2025

A hemispherical vessel is completely filled with a liquid of refractive index

\mu

. A small coin is kept at the lowest point (O) of the vessel as shown in figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point E (at the level of the vessel) is______.

(A) $\sqrt{3}$
(B) $\frac{3}{2}$
(C) $\sqrt{2}$
(D) $\frac{\sqrt{3}}{2}$

Q67·PhysicsSingle correctJEE Main 2025

A plano-convex lens having radius of curvature of first surface 2 cm exhibits focal length of

f_1

in air. Another plano-convex lens with first surface radius of curvature 3 cm has focal length of

f_2

when it is immersed in a liquid of refractive index 1.2. If both the lenses are made of same glass of refractive index 1.5, the ratio of

f_1

and

f_2

is :-

(A)3 : 5
(B)1 : 3
(C)1 : 2
(D)2 : 3

Q68·PhysicsSingle correctJEE Main 2025

A photograph of a landscape is captured by a drone camera at a height of 18 km. The size of the camera film is 2 cm

\times

2 cm and the area of the landscape photographed is 400 km

^2

. The focal length of the lens in the drone camera is :

(A)1.8 cm
(B)2.8 cm
(C)2.5 cm
(D)0.9 cm

Q69·PhysicsSingle correctJEE Main 2025

A thin plano convex lens made of glass of refractive index 1.5 is immersed in a liquid of refractive index 1.2. When the plane side of the lens is silver coated for complete reflection, the lens immersed in the liquid behaves like a concave mirror of focal length 0.2 m. The radius of curvature of the curved surface of the lens is :-

(A)0.15 m
(B)0.10 m
(C)0.20 m
(D)0.25 m

Q70·PhysicsSingle correctJEE Main 2025

What is the relative decrease in focal length of a lens for an increase in optical power by 0.1 D from 2.5 D ? [‘D’ stands for dioptre]

(A)0.04
(B)0.40
(C)0.1
(D)0.01

Q71·PhysicsSingle correctJEE Main 2025

What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness ‘h’ in terms of the angle of incidence ‘i’ and angle of refraction ‘r’, if the glass slab is placed in air medium ?

(A) $\dfrac{h\sin(i-r)}{\tan r}$
(B) $\dfrac{h\cos(i-r)}{\sin r}$
(C)h
(D) $\dfrac{h\sin(i-r)}{\cos r}$

Q72·PhysicsSingle correctJEE Main 2025

Given a thin convex lens (refractive index

\mu_2

), kept in a liquid (refractive index

\mu_1

,

\mu_1<\mu_2

) having radii of curvature

|R_1|

and

|R_2|

. Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place ?

(A) $\dfrac{\mu_1|R_1||R_2|}{\mu_2(|R_1|+|R_2|)-\mu_1|R_1|}$
(B) $\dfrac{\mu_1|R_1||R_2|}{\mu_2(|R_1|+|R_2|)-\mu_1|R_2|}$
(C) $\dfrac{\mu_1|R_1||R_2|}{\mu_2(2|R_1|+|R_2|)-\mu_1\sqrt{|R_1||R_2|}}$
(D) $\dfrac{(\mu_2+\mu_1)|R_1|}{\mu_2-\mu_1}$

Q73·PhysicsSingle correctJEE Main 2025

The refractive index of the material of a glass prism is

\sqrt3

. The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism?

(A) $50^\circ$
(B) $60^\circ$
(C) $58^\circ$
(D) $48^\circ$

Q74·PhysicsSingle correctJEE Main 2025

A spherical surface of radius of curvature

R

, separates air from glass (refractive index

=1.5

). The centre of curvature is in the glass medium. A point object ‘O’ placed in air on the optic axis of the surface, so that its real image is formed at ‘I’ inside glass. The line OI intersects the spherical surface at P and PO = PI. The distance PO equals to-

(A)5R
(B)3R
(C)2R
(D)1.5R

Q75·PhysicsSingle correctJEE Main 2025

A concave mirror of focal length

f

in air is dipped in a liquid of refractive index

\mu

. Its focal length in the liquid is :

(A) $\dfrac{f}{\mu}$
(B) $\dfrac{f}{\mu-1}$
(C) $\mu f$
(D) $f$

Q76·PhysicsSingle correctJEE Main 2025

A transparent film of refractive index, 2.0 is coated on a glass slab of refractive index, 1.45. What is the minimum thickness of transparent film to be coated for the maximum transmission of Green light of wavelength 550 nm. [Assume that the light is incident nearly perpendicular to the glass surface.]

(A)94.8 nm
(B)68.7 nm
(C)137.5 nm
(D)275 nm

Q77·PhysicsIntegerJEE Main 2025

The driver sitting inside a parked car is watching vehicles approaching from behind with the help of a convex side mirror of radius of curvature R = 2 m. A vehicle approaches from behind with a uniform speed of 90 km/h. When the vehicle is at a distance of 24 m, the magnitude of the acceleration of its image is a₀ m/s². The value of 100 a₀ is ______.

Q78·PhysicsSingle correctJEE Main 2025

Given is a thin convex lens of glass (refractive index μ) and both faces having radius of curvature R. It is silvered on one side to behave like a closed reflector. An object is placed on the optic axis so that the image gets formed on the object itself. The object distance is:

(A)R/μ
(B)R(2μ−3)
(C)R(2μ−1)
(D)R/(2μ−1)

Q79·PhysicsSingle correctJEE Main 2025

A symmetric thin biconvex lens is cut into four equal parts by two planes AB and CD as shown in figure. If the power of original lens is 4D then the power of a part of the divided lens is

(A)8D
(B)4D
(C)D
(D)2D

Q80·PhysicsSingle correctJEE Main 2025

In the arrangement shown in the figure there are three lenses formed by water (μ = 4/3) and glass (μ = 3/2) at the boundaries of a container; the thickness of glass is negligible compared to |R₁| and |R₂|, the radii of curvature of the upper and lower glass surfaces. The power of the combination is:

(A)−(1/6)(1/|R₁| + 1/|R₂|)
(B)−(1/6)(1/|R₁| − 1/|R₂|)
(C)(1/6)(1/|R₁| + 1/|R₂|)
(D)(1/6)(1/|R₁| − 1/|R₂|)

Q81·PhysicsNumericalJEE Advanced 2024

Two equilateral-triangular prisms

P_1

and

P_2

are kept with their sides parallel to each other, in vacuum, as shown in the figure. A light ray enters prism

P_1

at an angle of incidence θ such that the outgoing ray undergoes minimum deviation in prism

P_2

. If the respective refractive indices of

P_1

and

P_2

are

\sqrt{\frac{3}{2}}

and

\sqrt{3}

, then θ =

\sin^{-1}\left[\sqrt{\frac{3}{2}}\sin\left(\frac{\pi}{\beta}\right)\right]

, where the value of β is

Q82·PhysicsSingle correctJEE Advanced 2024

A light ray is incident on the surface of a sphere of refractive index

n

at an angle of incidence

\theta_{0}

. The ray partially refracts into the sphere with angle of refraction

\phi_{0}

and then partly reflects from the back surface. The reflected ray then emerges out of the sphere after a partial refraction. The total angle of deviation of the emergent ray with respect to the incident ray is

\alpha

. Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

List-I	List-II
P.If $n = 2$ and $\alpha = 180^{\circ}$ , then all the possible values of $\theta_{0}$ will be	1. $30^{\circ}$ and $0^{\circ}$
Q.If $n = \sqrt{3}$ and $\alpha = 180^{\circ}$ , then all the possible values of $\theta_{0}$ will be	2. $60^{\circ}$ and $0^{\circ}$
R.If $n = \sqrt{3}$ and $\alpha = 180^{\circ}$ , then all the possible values of $\phi_{0}$ will be	3. $45^{\circ}$ and $0^{\circ}$
S.If $n = \sqrt{2}$ and $\theta_{0} = 45^{\circ}$ , then all the possible values of $\alpha$ will be	4. $150^{\circ}$
	5. $0^{\circ}$

(A)P $\to$ 5; Q $\to$ 2; R $\to$ 1; S $\to$ 4
(B)P $\to$ 5; Q $\to$ 1; R $\to$ 2; S $\to$ 4
(C)P $\to$ 3; Q $\to$ 2; R $\to$ 1; S $\to$ 4
(D)P $\to$ 3; Q $\to$ 1; R $\to$ 2; S $\to$ 5

Q83·PhysicsMultiple correctJEE Advanced 2024

A glass beaker has a solid, plano-convex base of refractive index 1.60, as shown in the figure. The radius of curvature of the convex surface (SPU) is 9 cm, while the planar surface (STU) acts as a mirror. This beaker is filled with a liquid of refractive index

n

up to the level QPR. If the image of a point object

O

at a height of

h

(OT in the figure) is formed onto itself, then, which of the following option(s) is(are) correct?

(A)For $n = 1.42$ , $h = 50$ cm.
(B)For $n = 1.35$ , $h = 36$ cm.
(C)For $n = 1.45$ , $h = 65$ cm.
(D)For $n = 1.48$ , $h = 85$ cm.

Q84·PhysicsSingle correctJEE Main 2024

Given below are two statements: Statement (I): When an object is placed at the centre of curvature of a concave lens, image is formed at the centre of curvature of the lens on the other side. Statement (II): Concave lens always forms a virtual and erect image. In the light of the above statements, choose the correct answer from the options given below:

(A)Statement I is false but Statement II is true.
(B)Both Statement I and Statement II are false.
(C)Statement I is true but Statement II is false.
(D)Both Statement I and Statement II are true.

Q85·PhysicsSingle correctJEE Main 2024

The figure represents two biconvex lenses

L_{1}

and

L_{2}

having focal lengths 10 cm and 15 cm respectively. The distance between

L_{1}

and

L_{2}

is:

(A)10 cm
(B)15 cm
(C)5 cm
(D)35 cm

Q86·PhysicsSingle correctJEE Main 2024

The position of the image formed by the combination of lenses is:

(A)30 cm (right of third lens)
(B)15 cm (left of second lens)
(C)30 cm (left of third lens)
(D)15 cm (right of second lens)

Q87·PhysicsSingle correctJEE Main 2024

Critical angle of incidence for a pair of optical media is

45^\circ

. The refractive indices of first and second media are in the ratio:

(A) $\sqrt2:1$
(B) $1:2$
(C) $1:\sqrt2$
(D) $2:1$

Q88·PhysicsSingle correctJEE Main 2024

For the thin convex lens, the radii of curvature are at 15 cm and 30 cm respectively. The focal length the lens is 20 cm. The refractive index of the material is :

(A)1.2
(B)1.4
(C)1.5
(D)1.8

Q89·PhysicsNumericalJEE Main 2024

The refractive index of a prism is

\mu=\sqrt{3}

and the ratio of the angle of minimum deviation to the angle of the prism is one. The value of the angle of the prism is _______ degrees.

Q90·PhysicsSingle correctJEE Main 2024

Given below are two statements: Statement I: When white light is passed through a prism, the red light bends lesser than yellow and violet. Statement II: The refractive indices are different for different wavelengths in a dispersive medium. In the light of the above statements, choose the correct answer from the options given below:

(A)Both Statement I and Statement II are true.
(B)Statement I is true but Statement II is false.
(C)Both Statement I and Statement II are false.
(D)Statement I is false but Statement II is true.

Q91·PhysicsNumericalJEE Main 2024

A light ray is incident on a glass slab of thickness

4\sqrt{3}

cm and refractive index

\sqrt{2}

. The angle of incidence is equal to the critical angle for the glass slab with air. The lateral displacement of ray after passing through glass slab is ______ cm. (Given

\sin 15^{\circ}=0.25

)

Q92·PhysicsSingle correctJEE Main 2024

An effective power of a combination of

5

identical convex lenses which are kept in contact along the principal axis is

25\,D

. Focal length of each of the convex lens is:

(A) $20\,cm$
(B) $50\,cm$
(C) $500\,cm$
(D) $25\,cm$

Q93·PhysicsSingle correctJEE Main 2024

A monochromatic light of wavelength

6000\,\text{Å}

is incident on the single slit of width

0.01\,mm

. If the diffraction pattern is formed at the focus of the convex lens of focal length

20\,cm

, the linear width of the central maximum is:

(A) $60\,mm$
(B) $24\,mm$
(C) $120\,mm$
(D) $12\,mm$

Q94·PhysicsNumericalJEE Main 2024

The distance between object and its

3

times magnified real image as produced by a convex lens is

20\,cm

. The focal length of the lens used is ___

cm

.

Q95·PhysicsSingle correctJEE Main 2024

When unpolarized light is incident at an angle of

60^\circ

on a transparent medium from air. The reflected ray is completely polarized. The angle of refraction in the medium is

(A) $30^\circ$
(B) $60^\circ$
(C) $90^\circ$
(D) $45^\circ$

Q96·PhysicsNumericalJEE Main 2024

Light from a point source in air falls on a convex curved surface of radius 20 cm and refractive index 1.5. If the source is located at 100 cm from the convex surface, the image will be formed at ______ cm from the object.

Q97·PhysicsSingle correctJEE Main 2024

The refractive index of a prism with apex angle A is

\cot\dfrac{A}{2}

. The angle of minimum deviation is :

(A) $\delta_m=180^\circ-A$
(B) $\delta_m=180^\circ-3A$
(C) $\delta_m=180^\circ-4A$
(D) $\delta_m=180^\circ-2A$

Q98·PhysicsNumericalJEE Main 2024

In an experiment to measure the focal length (f) of a convex lens, the magnitude of object distance (x) and the image distance (y) are measured with reference to the focal point of the lens. The y-x plot is shown in figure. The focal length of the lens is ______ cm.

Q99·PhysicsNumericalJEE Main 2024

The distance between object and its two times magnified real image as produced by a convex lens is

45\,cm

. The focal length of the lens used is ___

cm

.

Q100·PhysicsSingle correctJEE Main 2024

The diffraction pattern of a light of wavelength

400\,nm

diffracting from a slit of width

0.2\,mm

is focused on the focal plane of a convex lens of focal length

100\,cm

. The width of the

1^{st}

secondary maxima will be:

(A) $2\,mm$
(B) $2\,cm$
(C) $0.02\,mm$
(D) $0.2\,mm$

Q101·PhysicsSingle correctJEE Main 2024

If the distance between object and its two times magnified virtual image produced by a curved mirror is 15 cm, the focal length of the mirror must be:

(A)15 cm
(B) $-12$ cm
(C) $-10$ cm
(D) $\dfrac{10}{3}$ cm

Q102·PhysicsSingle correctJEE Main 2024

A convex mirror of radius of curvature 30 cm forms an image that is half the size of the object. The object distance is :

(A) $-15$ cm
(B) $45$ cm
(C) $-45$ cm
(D) $15$ cm

Q103·PhysicsSingle correctJEE Main 2024

A biconvex lens of refractive index 1.5 has a focal length of 20 cm in air. Its focal length when immersed in a liquid of refractive index 1.6 will be:

(A) $-16$ cm
(B) $-160$ cm
(C) $+160$ cm
(D) $+16$ cm

Q104·PhysicsNumericalJEE Main 2024

Two immiscible liquids of refractive indices

\dfrac{8}{5}

and

\dfrac{3}{2}

respectively are put in a beaker as shown in the figure. The height of each column is 6 cm. A coin is placed at the bottom of the beaker. For near normal vision, the apparent depth of the coin is

\dfrac{\alpha}{4}

cm. The value of

\alpha

is __________.

Q105·PhysicsSingle correctJEE Main 2024

If the refractive index of the material of a prism is

\cot\!\left(\dfrac{A}{2}\right)

, where

A

is the angle of prism then the angle of minimum deviation will be:

(A) $\pi-2A$
(B) $\dfrac{\pi}{2}-2A$
(C) $\pi-A$
(D) $\dfrac{\pi}{2}-A$

Q106·PhysicsNumericalJEE Main 2024

A parallel beam of monochromatic light of wavelength 5000

\mathring{A}

is incident normally on a single narrow slit of width 0.001 mm. The light is focused by convex lens on screen, placed on its focal plane. The first minima will be formed for the angle of diffraction of ________ (degree).

Q107·PhysicsMultiple correctJEE Advanced 2023

A plane polarized blue light ray is incident on a prism such that there is no reflection from the surface of the prism. The angle of deviation of the emergent ray is

\delta = 60^\circ

(see Figure-1). The angle of minimum deviation for red light from the same prism is

\delta_{min} = 30^\circ

(see Figure-2). The refractive index of the prism material for blue light is

\sqrt{3}

. Which of the following statement(s) is(are) correct?

(A)The blue light is polarized in the plane of incidence.
(B)The angle of the prism is $45^\circ$ .
(C)The refractive index of the material of the prism for red light is $\sqrt{2}$ .
(D)The angle of refraction for blue light in air at the exit plane of the prism is $60^0$

Q108·PhysicsMultiple correctJEE Advanced 2023

A monochromatic light wave is incident normally on a glass slab of thickness d, as shown in the figure. The refractive index of the slab increases linearly from

n_1

to

n_2

over the height h. Which of the following statement(s) is(are) true about the light wave emerging out of the slab?

(A)It will deflect up by an angle $\tan^{-1}\left[\frac{\left(n_2^{2} - n_1^{2}\right)d}{2h}\right]$ .
(B)It will deflect up by an angle $\tan^{-1}\left[\frac{\left(n_2 - n_1\right)d}{h}\right]$ .
(C)It will not deflect.
(D)The deflection angle depends only on $(n_2 - n_1)$ and not on the individual values of $n_1$ and $n_2$ .

Q109·PhysicsNumericalJEE Main 2023

The refractive index of a transparent liquid filled in an equilateral hollow prism is

\sqrt{2}

. The angle of minimum deviation for the liquid will be __________

^\circ

.

Q110·PhysicsSingle correctJEE Main 2023

A vessel of depth

'd'

is half filled with oil of refractive index

n_{1}

and the other half is filled with water of refractive index

n_{2}

. The apparent depth of this vessel when viewed from above will be:

(A) $\dfrac{d\,n_{1}n_{2}}{(n_{1}+n_{2})}$
(B) $\dfrac{d(n_{1}+n_{2})}{2n_{1}n_{2}}$
(C) $\dfrac{d\,n_{1}n_{2}}{2(n_{1}+n_{2})}$
(D) $\dfrac{2d(n_{1}+n_{2})}{n_{1}n_{2}}$

Q111·PhysicsNumericalJEE Main 2023

A fish rising vertically upward with a uniform velocity of

8\,ms^{-1}

, observes that a bird is diving vertically downward towards the fish with the velocity of

12\,ms^{-1}

. If the refractive index of water is

\dfrac{4}{3}

, then the actual velocity of the diving bird to pick the fish, will be _____

ms^{-1}

.

Q112·PhysicsNumericalJEE Main 2023

A biconvex lens of focal length 10 cm is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is ____ D.

Q113·PhysicsSingle correctJEE Main 2023

An ice cube has a bubble inside. When viewed from one side the apparent distance of the bubble is 12 cm. When viewed from the opposite side, the apparent distance of the bubble is observed as 4 cm. If the side of the ice cube is 24 cm, the refractive index of the ice cube is

(A) $\dfrac43$
(B) $\dfrac32$
(C) $\dfrac23$
(D) $\dfrac65$

Q114·PhysicsNumericalJEE Main 2023

Two convex lenses of focal length 20 cm each are placed coaxially with a separation of 60 cm between them. The image of the distant object formed by the combination is at _________ cm from the first lens.

Q115·PhysicsSingle correctJEE Main 2023

The critical angle for a denser-rarer interface is 45

^\circ

. The speed of light in rarer medium is

3 \times 10^8

m/s. The speed of light in the denser medium is:

(A) $5 \times 10^7$ m/s
(B) $2.12 \times 10^8$ m/s
(C) $3.12 \times 10^7$ m/s
(D) $\sqrt{2} \times 10^8$ m/s

Q116·PhysicsNumericalJEE Main 2023

The radius of curvature of each surface of a convex lens having refractive index 1.8 is 20 cm. The lens is now immersed in a liquid of refractive index 1.5. The ratio of power of lens in air to its power in the liquid will be

x : 1

. The value of x is ______.

Q117·PhysicsSingle correctJEE Main 2023

A ray of light is reflected from a plane mirror with

30^\circ

angle of reflection. The angle of deviation of the ray after reflection is:

(A) $60^\circ$
(B) $120^\circ$
(C) $110^\circ$
(D) $130^\circ$

Q118·PhysicsNumericalJEE Main 2023

As shown in the figure, a plane mirror is fixed at a height of

50

cm from the bottom of a tank containing water

\left(\mu=\dfrac{4}{3}\right)

. The height of water in the tank is

8

cm. A small bulb is placed at the bottom of the water tank. The distance of the image of the bulb formed by the mirror from the bottom of the tank is ____ cm.

Q119·PhysicsSingle correctJEE Main 2023

An object is placed at a distance of 12 cm in front of a plane mirror. The virtual and erect image is formed by the mirror. Now the mirror is moved by 4 cm towards the stationary object. The distance by which the position of image would be shifted, will be:

(A)4 cm towards mirror
(B)8 cm towards mirror
(C)8 cm away from mirror
(D)4 cm away from mirror

Q120·PhysicsNumericalJEE Main 2023

A point object

O

is placed in front of two thin symmetrical coaxial convex lenses

L_1

and

L_2

with focal lengths

24

cm and

9

cm respectively. The distance between the two lenses is

10

cm and the object is placed

6

cm away from lens

L_1

as shown in the figure. The distance between the object and the image formed by the system of two lenses is _______ cm.

Q121·PhysicsNumericalJEE Main 2023

Two vertical parallel mirrors A and B are separated by

10\,\text{cm}

. A point object O is placed at a distance of

2\,\text{cm}

from mirror A. The distance of the second nearest image behind mirror A from the mirror A is ______

\text{cm}

Q122·PhysicsNumericalJEE Main 2023

Two transparent media having refractive indices 1.0 and 1.5 are separated by a spherical refracting surface of radius of curvature 30 cm. The centre of curvature of the surface is towards the denser medium and a point object is placed on the principal axis in the rarer medium at a distance of 15 cm from the pole of the surface. The distance of the image from the pole of the surface is ____ cm.

Q123·PhysicsSingle correctJEE Main 2023

In a reflecting telescope, a secondary mirror is used to:

(A)reduce the problem of mechanical support
(B)remove spherical aberration
(C)make chromatic aberration zero
(D)move the eyepiece outside the telescopic tube

Q124·PhysicsSingle correctJEE Main 2023

A monochromatic light wave with wavelength

\lambda_1

and frequency

v_1

in air enters another medium. The angle of incidence and angle of refraction at the interface are

45^\circ

and

30^\circ

respectively. The wavelength

\lambda_2

and frequency

v_2

of the refracted wave are:

(A) $\lambda_2=\lambda_1,\,v_2=\sqrt2v_1$
(B) $\lambda_2=\dfrac{1}{\sqrt2}\lambda_1,\,v_2=v_1$
(C) $\lambda_2=\sqrt2\lambda_1,\,v_2=v_1$
(D) $\lambda_2=\lambda_1,\,v_2=\dfrac{1}{\sqrt2}v_1$

Q125·PhysicsNumericalJEE Main 2023

A pole is vertically submerged in swimming pool, such that it gives a length of shadow

2.15\,m

within water when sunlight is incident at an angle of

30^\circ

with the surface of water. If swimming pool is filled to a height of

1.5\,m

, then the height of the pole above the water surface in centimetres is _____ (

n_w=4/3

).

Q126·PhysicsNumericalJEE Main 2023

A thin cylindrical rod of length

10

cm is placed horizontally on the principal axis of a concave mirror of focal length

20

cm. The rod is placed in such a way that mid point of the rod is at

40

cm from the pole of mirror. The length of the image formed by the mirror will be

\tfrac{x}{3}

cm. The value of

x

is _______ .

Q127·PhysicsSingle correctJEE Main 2023

Two objects A and B are placed at

15

cm and

25

cm from the pole in front of a concave mirror having radius of curvature

40

cm. The distance between images formed by the mirror is _________.

(A) $100$ cm
(B) $60$ cm
(C) $160$ cm
(D) $40$ cm

Q128·PhysicsSingle correctJEE Main 2023

A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index

\dfrac53

is poured inside the bucket, then microscope have to be raised by

30

cm to focus the object again. The height of the liquid in the bucket is:

(A) $12$ cm
(B) $50$ cm
(C) $18$ cm
(D) $75$ cm

Q129·PhysicsNumericalJEE Main 2023

In a medium the speed of light wave decreases to

0.2

times to its speed in free space. The ratio of relative permittivity to the refractive index of the medium is

x:1

. The value of

x

is (Given speed of light in free space

= 3 \times 10^8\,\text{m s}^{-1}

and for the given medium

\mu_r = 1

)

Q130·PhysicsSingle correctJEE Main 2023

A thin prism

P_1

with an angle

6^{\circ}

and made of glass of refractive index 1.54 is combined with another prism

P_2

made from glass of refractive index 1.72 to produce dispersion without average deviation. The angle of prism

P_2

is:

(A) $1.3^{\circ}$
(B) $6^{\circ}$
(C) $4.5^{\circ}$
(D) $7.8^{\circ}$

Q131·PhysicsSingle correctJEE Main 2023

A person has been using spectacles of power

-1.0

dioptre for distant vision and a separate reading glass of power

2.0

dioptres. What is the least distance of distinct vision for this person:

(A) $40$ cm
(B) $30$ cm
(C) $10$ cm
(D) $50$ cm

Q132·PhysicsNumericalJEE Main 2023

Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are

2.8

(medium

-1

) and

6.8

(medium

-2

), respectively. To satisfy the condition, so that the reflected and refracted rays are perpendicular to each other, the angle of incidence should be

\tan^{-1}\left(1+\dfrac{10}{n}\right)^{1/2}

the value of

\theta

is _____. (Given for dielectric media,

\mu_r=1

)

Q133·PhysicsSingle correctJEE Main 2023

Which of the following are true? A. Speed of light in vacuum is dependent on the direction of propagation. B. Speed of light in a medium is independent of the wavelength of light. C. The speed of light is independent of the motion of the source. D. The speed of light in a medium is independent of intensity. Choose the correct answer from the options given below:

(A)C and D only
(B)B and C only
(C)A and C only
(D)B and D only

Q134·PhysicsSingle correctJEE Main 2023

The light rays from an object have been reflected towards an observer from a standard flat mirror, the image observed by the observer are: A. Real B. Erect C. Smaller in size then object D. Laterally inverted Choose the most appropriate answer from the options given below:

(A)A, C, and D Only
(B)B and D Only
(C)A and D Only
(D)B and C Only

Q135·PhysicsNumericalJEE Main 2023

An object is placed on the principal axis of convex lens of focal length 10 cm as shown. A plane mirror is placed on the other side of lens at a distance of 20 cm. The image produced by the plane mirror is 5 cm inside the mirror. The distance of the object from the lens is ______ cm.

Q136·PhysicsNumericalJEE Main 2023

A ray of light is incident from air on a glass plate having thickness

\sqrt{3}

cm and refractive index

\sqrt{2}

. The angle of incidence of the ray is equal to the critical angle for the glass-air interface. The lateral displacement of the ray when it passes through the plate is _______

\times10^{-2}

cm. (Given

\sin 15^{\circ}=0.26

)

Q137·PhysicsNumericalJEE Main 2023

As shown in the figure, a combination of a thin plano concave lens and a thin plano convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is 30 cm and refraction index of the material for both the lenses is 1.75. Both the lenses are placed at distance of 40 cm from each other. Due to the combination, the image of the object is formed at distance = _______ cm, from concave lens.

Q138·PhysicsNumericalJEE Main 2023

A convex lens of refractive index

1.5

and focal length

18

cm in air is immersed in water. The change in focal length of the lens will be _________ cm. (Given refractive index of water

=\dfrac43

)

Q139·PhysicsSingle correctJEE Main 2023

When a beam of white light is allowed to pass through convex lens parallel to principal axis, the different colours of light converge at different point on the principle axis after refraction. This is called:

(A)Spherical aberration
(B)Polarisation
(C)Chromatic aberration
(D)Scattering

Q140·PhysicsMultiple correctJEE Advanced 2022

Three plane mirrors form an equilateral triangle with each side of length L. There is a small hole at a distance

l > 0

from one of the corners as shown in the figure. A ray of light is passed through the hole at an angle

\theta

and can only come out through the same hole. The cross section of the mirror configuration and the ray of light lie on the same plane. Which of the following statement(s) is(are) correct?

(A)The ray of light will come out for $\theta = 30^\circ$ , for $0 < l < L$ .
(B)There is an angle for $l = \frac{L}{2}$ at which the ray of light will come out after two reflections.
(C)The ray of light will NEVER come out for $\theta = 60^\circ$ , and $l = \frac{L}{3}$
(D)The ray of light will come out for $\theta= 60^\circ$ , and $0 < l < \frac{L}{2}$ after six reflections.

Q141·PhysicsIntegerJEE Advanced 2022

An object and a concave mirror of focal length f=10cm both move along the principal axis of the mirror with constant speeds. The object moves with speed V

_0

=15 cm s

^{-1}

towards the mirror with respect to a laboratory frame. The distance between the object and the mirror at a given moment is denoted by u . When u=30 cm , the speed of the mirror V

_m

is such that the image is instantaneously at rest with respect to the laboratory frame, and the object forms a real image. The magnitude of V

_m

is _________ cms

^{-1}

Q142·PhysicsNumericalJEE Advanced 2022

A rod of length 2 cm makes an angle

\frac{2\pi}{3}

rad with the principal axis of a thin convex lens. The lens has a focal length of 10 cm and is placed at a distance of

\frac{40}{3}

cm from the object as shown in the figure, The height of the image is

\frac{30\sqrt{3}}{13}

and the angle made by it with respect to the principal axis is

\alpha

rad. The value of

\alpha

is

\frac{\pi}{n}\ rad

, where n is ___________

Q143·PhysicsIntegerJEE Advanced 2022

Consider a configuration of n identical units, each consisting of three layers. The first layer is a column of air of height

h = \frac{1}{3}

cm, and the second and third layers are of equal thickness

d = \frac{\sqrt{3}-1}{2}

cm , and refractive indices

\mu_1 = \sqrt{\frac{3}{2}}

and μ

_2

=

\sqrt{3}

, respectively. A light source O is placed on the top of the first unit, as shown in the figure. A ray of light from O is incident on the second layer of the first unit at an angle of θ=60° to the normal. For a specific value of n , the ray of light emerges from the bottom of the configuration at a distance

l = \frac{8}{\sqrt{3}}

cm, as shown in the figure. The value of n is___________.

Q144·PhysicsNumericalJEE Main 2022

The X-Y plane be taken as the boundary between two transparent media

M_1

and

M_2

.

M_1

in

Z \geq 0

has a refractive index of

\sqrt{2}

and

M_2

with

Z < 0

has a refractive index of

\sqrt{3}

. A ray of light travelling in

M_1

along the direction given by the vector

\vec{A} = 4\sqrt{3}\hat{i} - 3\sqrt{3}\hat{j} - 5\hat{k}

, is incident on the plane of separation. The value of difference between the angle of incident in

M_1

and the angle of refraction in

M_2

will be ______________ degree.

Q145·PhysicsSingle correctJEE Main 2022

Light enters from air into a given medium at an angle of 45° with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of 15° from its original direction. The refractive index of the medium is :

(A)1.732
(B)1.333
(C)1.414
(D)2.732

Q146·PhysicsSingle correctJEE Main 2022

In normal adjustment, for a refracting telescope, the distance between objective and eye piece is 30 cm. The focal length of the objective, when the angular magnification of the telescope is 2, will be:

(A)20 cm
(B)30 cm
(C)10 cm
(D)15 cm

Q147·PhysicsNumericalJEE Main 2022

An object 'o' is placed at a distance of 100 cm in front of a concave mirror of radius of curvature 200 cm as shown in the figure. The object starts moving towards the mirror at a speed 2 cm/s. The position of the image from the mirror after 10s will be at ....... cm.

Q148·PhysicsNumericalJEE Main 2022

In an experiment with a convex lens. The plot of the image distance (v') against the object distance (

\mu

') measured from the focus gives a curve v'

\mu

' = 225. If all the distances are measured in cm. The magnitude of the focal length of the lens is .......... cm.

Q149·PhysicsSingle correctJEE Main 2022

The power of a lens (biconvex) is 1.25

m^{-1}

in particular medium. Refractive index of the lens is 1.5 and radii of curvature are 20 cm and 40 cm respectively. The refractive index of surrounding medium :

(A)1.0
(B) $\dfrac{9}{7}$
(C) $\dfrac{3}{2}$
(D) $\dfrac{4}{3}$

Q150·PhysicsSingle correctJEE Main 2022

As shown in the figure, after passing through the medium 1. The speed of light v

_{2}

in medium 2 will be : (Given c = 3 × 10

^{8}

ms

^{-1}

)

(A)1.0 × 10 $^{8}$ ms $^{-1}$
(B)0.5 × 10 $^{8}$ ms $^{-1}$
(C)1.5 × 10 $^{8}$ ms $^{-1}$
(D)3.0 × 10 $^{8}$ ms $^{-1}$

Q151·PhysicsNumericalJEE Main 2022

A thin prism of angle 6° and refractive index for yellow light (n

_Y

)1.5 is combined with another prism of angle 5° and n

_Y

= 1.55. The combination produces no dispersion. The net average deviation (δ) produced by the combination is

\left(\frac{1}{x}\right)^{\circ}

. The value of x is…….

Q152·PhysicsNumericalJEE Main 2022

In the given figure, the face AC of the equilateral prism is immersed in a liquid of refractive index 'n'. For incident angle 60° at the side AC, the refracted light beam just grazes along face AC. The refractive index of the liquid

n = \frac{\sqrt{x}}{4}

. The value of x is__________ . (Given refractive index of glass = 1.5)

Q153·PhysicsNumericalJEE Main 2022

The graph between

\frac{1}{u}

and

\frac{1}{v}

for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of length is 1.5 and its both the surfaces have same radius of curvatures R. The value of R will be _____cm. (Where u = object distance , v = image distance)

Q154·PhysicsSingle correctJEE Main 2022

Light travels in two media

M_1

and

M_2

with speeds

1.5 \times 10^{8}\ \text{ms}^{-1}

and

2.0 \times 10^{8}\ \text{ms}^{-1}

respectively. The critical angle between them is:

(A) $\tan^{-1}\left(\frac{3}{\sqrt{7}}\right)$
(B) $\tan^{-1}\left(\frac{2}{3}\right)$
(C) $\cos^{-1}\left(\frac{3}{4}\right)$
(D) $\sin^{-1}\left(\frac{2}{3}\right)$

Q155·PhysicsSingle correctJEE Main 2022

Time taken by light to travel in two different materials A and B of refractive indices

\mu_A

and

\mu_B

of same thickness is

t_1

and

t_2

respectively. If

t_2 - t_1 = 5 \times 10^{-10}

s and the ratio of

\mu_A

to

\mu_B

is 1 : 2. Then the thickness of material, in meter is : (Given

v_A

and

v_B

are velocities of light in A and B materials respectively).

(A) $5 \times 10^{-10} v_a$ m
(B) $5 \times 10^{-10}$ m
(C) $1.5 \times 10^{-10}$ m
(D) $5 \times 10^{-10} v_B$ m

Q156·PhysicsSingle correctJEE Main 2022

Which of the following statement is correct ?

(A)In primary rainbow, observer sees red colour on the top and violet on the bottom
(B)In primary rainbow, observer sees violet colour on the top and red on the bottom
(C)In primary rainbow, light wave suffers total internal reflection twice before coming out of water drops
(D)Primary rainbow is less bright than secondary rainbow.

Q157·PhysicsSingle correctJEE Main 2022

The speed of light in media 'A' and 'B' are

2.0 \times 10^{10}

cm/s and

1.5 \times 10^{10}

chm/s respectively. A ray of light enters from the medium B to A at an incident angle 'θ'. If the ray suffers total internal reflection, then

(A) $\theta = \sin^{-1}\left(\frac{3}{4}\right)$
(B) $\theta > \sin^{-1}\left(\frac{2}{3}\right)$
(C) $\theta < \sin^{-1}\left(\frac{3}{4}\right)$
(D) $\theta > \sin^{-1}\left(\frac{3}{4}\right)$

Q158·PhysicsNumericalJEE Main 2022

A parallel beam of light is allowed to fall on a transparent spherical globe of diameter 30 cm and refractive index 1.5. The distance from the centre of the globe at which the beam of light can converge is _________ mm.

Q159·PhysicsSingle correctJEE Main 2022

The refracting angle of a prism is A and refractive index of the material of the prism is cot (A/2). Then the angle of minimum deviation will be -

(A)180 – 2A
(B)90 – A
(C)180 + 2A
(D)180 – 3A

Q160·PhysicsSingle correctJEE Main 2022

Consider a light ray travelling in air is incident into a medium of refractive index

\sqrt{2n}

. The incident angle is twice that of refracting angle. Then, the angle of incidence will be :

(A) $\sin^{-1}\left(\sqrt{n}\right)$
(B) $\cos^{-1}\left(\sqrt{\frac{n}{2}}\right)$
(C) $\sin^{-1}\left(\sqrt{2n}\right)$
(D) $2\cos^{-1}\left(\sqrt{\frac{n}{2}}\right)$

Q161·PhysicsSingle correctJEE Main 2022

A convex lens has power P. It is cut into two halves along its principal axis. Further one piece (out of the two halves) is cut into two halves perpendicular to the principal axis (as shown in figure). Choose the incorrect option for the reported pieces.

(A)Power of $L_{1} = \dfrac{P}{2}$
(B)Power of $L_{2} = \dfrac{P}{2}$
(C)Power of $L_{3} = \dfrac{P}{2}$
(D)Power of $L_{1} = P$

Q162·PhysicsNumericalJEE Main 2022

A small bulb is placed at the bottom of a tank containing water to a depth of

\sqrt{7}

m. The refractive index of water is

\frac{4}{3}

. The area of the surface of water through which light from the bulb can emerge out is xπ m

^{2}

. The value of x is________.

Q163·PhysicsNumericalJEE Main 2022

A light ray is incident, at an incident angle

\theta_{1}

, on the system of two plane mirrors

M_{1}

and

M_{2}

having an inclination angle 75° between them (as shown in figure). After reflecting from mirror

M_{1}

it gets reflected back by the mirror

M_{2}

with an angle of reflection 30°. The total deviation of the ray will be .............. degree.

Q164·PhysicsSingle correctJEE Main 2022

A light wave travelling linearly in a medium of dielectric constant 4, incident on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be (Given : relative permeability of medium

\mu_r

= 1)

(A)10°
(B)20°
(C)30°
(D)60°

Q165·PhysicsSingle correctJEE Main 2022

The difference of speed of light in the two media A and B

(v_{A} - v_{B})

is

2.6 \times 10^{7}

m/s. If the refractive index of medium B is 1.47, then the ratio of refractive index of medium B to medium A is : (Given : speed of light in vacuum

c = 3 \times 10^{8}\ \mathrm{ms}^{-1}

)

(A)1.303
(B)1.318
(C)1.13
(D)0.12

Q166·PhysicsNumericalJEE Main 2022

A ray of ligh is incident at an angle of incidence

60^\circ

on the glass slab of refractive index

\sqrt{3}

. After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray is

4\sqrt{3}

cm. The thickness of the glass slab is ______ cm.

Q167·PhysicsNumericalJEE Main 2022

Two identical thin biconvex lenses of focal length 15 cm and refractive index 1.5 are in contact with each other. The space between the lenses is filled with a liquid of refractive index 1.25. The focal length of the combination is _______ cm.

Q168·PhysicsMultiple correctJEE Advanced 2021

For a prism of prism angle

\theta = 60^{\circ}

, the refractive indices of the left half and the right half are, respectively,

n_1

and

n_2

(

n_2 \geq n_1

) as shown in the figure. The angle of incidence

i

is chosen such that the incident light rays will have minimum deviation if

n_1 = n_2 = n = 1.5

. For the case of unequal refractive indices,

n_1 = n

and

n_2 = n + \Delta n

(where

\Delta n << n

), the angle of emergence

e = i + \Delta e

. Which of the following statement(s) is (are) correct ?

(A)The value of $\Delta e$ (in radians) is greater than that of $\Delta n$
(B) $\Delta e$ is proportional to $\Delta n$
(C) $\Delta e$ lies between 2.0 and 3.0 milliradians, if $\Delta n = 2.8 \times 10^{-3}$
(D) $\Delta e$ lies between 1.0 and 1.6 milliradians, if $\Delta n = 2.8 \times 10^{-3}$

Q169·PhysicsMultiple correctJEE Advanced 2021

A wide slab consisting of two media of refractive indices

n_1

and

n_2

is placed in air as shown in the figure. A ray of light is incident from medium

n_1

to

n_2

at an angle

\theta

, where

\sin\theta

is slightly larger than

1/n_1

. Take refractive index of air as 1. Which of the following statement(s) is(are) correct?

(A)The light ray enters air if $n_2 = n_1$
(B)The light ray is finally reflected back into the medium of refractive index $n_1$ if $n_2 < n_1$
(C)The light ray is finally reflected back into the medium of refractive index $n_1$ if $n_2 > n_1$
(D)The light ray is reflected back into the medium of refractive index $n_1$ if $n_2 = 1$

Q170·PhysicsSingle correctJEE Advanced 2021

An extended object is placed at point O, 10 cm in front of a convex lens

L_1

and a concave lens

L_2

is placed 10 cm behind it, as shown in the figure. The radii of curvature of all the curved surfaces in both the lenses are 20 cm. The refractive index of both the lenses is 1.5. The total magnification of this lens system is

(A)0.4
(B)0.8
(C)1.3
(D)1.6

Q171·PhysicsSingle correctJEE Main 2021

A glass tumbler having inner depth of 17.5 cm is kept on a table. A student starts pouring water (μ = 4/3) into it while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled ?

(A)11.7 cm
(B)10 cm
(C)7.5 cm
(D)8.75 cm

Q172·PhysicsNumericalJEE Main 2021

Cross-section view of a prism is the equilateral triangle ABC in the figure. The minimum deviation is observed using this prism when the angle of incidence is equal to the prism angle. The time taken by light to travel from P (midpoint of BC) to A is______

\times

10

^{-10}

s. (Given, speed of light in vacuum = 3

\times

10

^{8}

m/s and

\cos 30^\circ = \frac{\sqrt{3}}{2}

)

Q173·PhysicsSingle correctJEE Main 2021

An object is placed at the focus of concave lens having focal length

f

. What is the magnification and distance of the image from the optical centre of the lens?

(A)1, $\infty$
(B)Very high, $\infty$
(C) $\frac{1}{2},\frac{f}{2}$
(D) $\frac{1}{4},\frac{f}{4}$

Q174·PhysicsSingle correctJEE Main 2021

Two plane mirrors

M_{1}

and

M_{2}

are at right angle to each other shown. A point source 'P' is placed at 'a' and '2a' meter away from

M_{1}

and

M_{2}

respectively. The shortest distance between the images thus formed is : (Take

\sqrt{5}

= 2.3)

(A)3a
(B)4.6 a
(C)2.3 a
(D) $2\sqrt{10}$ a

Q175·PhysicsSingle correctJEE Main 2021

Curved surfaces of a plano-convex lens of refractive index

\mu_{1}

and a plano-concave lens of refractive index

\mu_{2}

have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the combined lenses.

(A) $\frac{1}{\mu_{2}-\mu_{1}}$
(B) $\mu_{1}-\mu_{2}$
(C) $\frac{1}{\mu_{1}-\mu_{2}}$
(D) $\mu_{2}-\mu_{1}$

Q176·PhysicsSingle correctJEE Main 2021

An object is placed beyond the centre of curvature C of the given concave mirror. If the distance of the object is

d_1

from C and the distance of the image formed is

d_2

from C, the radius of curvature of this mirror is :

(A) $\frac{2d_1d_2}{d_1 - d_2}$
(B) $\frac{2d_1d_2}{d_1 + d_2}$
(C) $\frac{d_1d_2}{d_1 + d_2}$
(D) $\frac{d_1d_2}{d_1 - d_2}$

Q177·PhysicsSingle correctJEE Main 2021

Find the distance of the image from object O, formed by the combination of lenses in the figure :

(A)75 cm
(B)10 cm
(C)20 cm
(D)infinity

Q178·PhysicsSingle correctJEE Main 2021

Car B overtakes another car A at a relative speed of 40

ms^{-1}

. How fast will the image of car B appear to move in the mirror of focal length 10 cm fitted in car A, when the car B is 1.9 m away from the car A?

(A)4 $ms^{-1}$
(B)0.2 $ms^{-1}$
(C)40 $ms^{-1}$
(D)0.1 $ms^{-1}$

Q179·PhysicsNumericalJEE Main 2021

An object is placed at a distance of 12 cm from a convex lens. A convex mirror of focal length 15 cm is placed on other side of lens at 8 cm as shown in the figure. Image of object coincides with the object. When the convex mirror is removed, a real and inverted image is formed at a position. The distance of the image from the object will be ........(cm)

Q180·PhysicsNumericalJEE Main 2021

A prism of refractive index

n_1

and another prism of refractive index

n_2

are stuck together (as shown in the figure).

n_1

and

n_2

depend on λ, the wavelength of light, according to the relation

n_1 = 1.2 + \frac{10.8 \times 10^{-14}}{\lambda^2}

and

n_2 = 1.45 + \frac{1.8 \times 10^{-14}}{\lambda^2}

The wavelength for which rays incident at any angle on the interface BC pass through without bending at that interface will be ____ nm.

Q181·PhysicsSingle correctJEE Main 2021

The expected graphical representation of the variation of angle of deviation 'δ' with angle of incidence 'i' in a prism is :

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q182·PhysicsSingle correctJEE Main 2021

A ray of light entering from air into a denser medium of refractive index

\frac{4}{3}

, as shown in figure. The light ray suffers total internal reflection at the adjacent surface as shown. The maximum value of angle

\theta

should be equal to :

(A) $\sin^{-1}\frac{\sqrt{5}}{4}$
(B) $\sin^{-1}\frac{\sqrt{7}}{3}$
(C) $\sin^{-1}\frac{\sqrt{7}}{4}$
(D) $\sin^{-1}\frac{\sqrt{5}}{3}$

Q183·PhysicsSingle correctJEE Main 2021

A prism of refractive index

\mu

and angle of prism A is placed in the position of minimum angle of deviation. If minimum angle of deviation is also A, then in terms of refractive index value of A is :

(A) $2\cos^{-1}\left(\frac{\mu}{2}\right)$
(B) $\cos^{-1}\left(\frac{\mu}{2}\right)$
(C) $\sin^{-1}\left(\frac{\mu}{2}\right)$
(D) $\sin^{-1}\left(\sqrt{\frac{\mu-1}{2}}\right)$

Q184·PhysicsSingle correctJEE Main 2021

A ray of laser of a wavelength 630 nm is incident at an angle of 30° at the diamond- air interface. It is going from diamond to air. The refractive index diamond is 2.42 and that of air is 1. Choose the correct option.

(A)angle of refraction is 53.4°
(B)angle of refraction is 30°
(C)angle of refraction is 24.41°
(D)refraction is not possible

Q185·PhysicsSingle correctJEE Main 2021

A ray of light passes from a denser medium to a rarer medium at an angle of incidence i. The reflected and refracted rays make an angle of 90° with each other. The angle of reflection and refraction are respectively r and r′. The critical angle is given by :

(A) $\sin^{-1}(\cot r)$
(B) $\tan^{-1}(\sin i)$
(C) $\sin^{-1}(\tan r')$
(D) $\sin^{-1}(\tan r)$

Q186·PhysicsNumericalJEE Main 2021

A ray of light passing through a prism

\left(\mu = \sqrt{3}\right)

surface minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. Then, the angle of prism is ________ (in degrees).

Q187·PhysicsSingle correctJEE Main 2021

Region I and II are separated by a spherical surface of radius 25 cm. An object is kept in region I at a distance of 40 cm from the surface. The distance of the image from the surface is :

(A)9.52 cm
(B)18.23 cm
(C)37.58 cm
(D)55.44 cm

Q188·PhysicsNumericalJEE Main 2021

An object viewed from a near point distance of 25 cm, using a microscopic lens with magnification '6', gives an unresolved image, A resolved image is observed at infinite distance with a total magnification double the earlier using an eyepiece along with the given lens and a tube of length 0.6 m, if the focal length of the eyepiece is equal to _________ cm.

Q189·PhysicsSingle correctJEE Main 2021

Three rays of light, namely red (R), green (G) and blue (B) are incident on the face PQ of a right angled prism PQR as shown in figure. The refractive indices of the material of the prism for red, green and blue wavelength are 1.27, 1.42 and 1.49 respectively. The colour of the ray(s) emerging out of the face PR is :

(A)green
(B)red
(C)blue and green
(D)blue

Q190·PhysicsSingle correctJEE Main 2021

Your friend is having eye sight problem. She is not able to see clearly a distant uniform window mesh and it appears to her as non-uniform and distorted. The doctor diagnosed the problem as :

(A)Astigmatism
(B)Myopia with Astigmatism
(C)Presbyopia with Astigmatism
(D)Myopia and hypermetropia

Q191·PhysicsNumericalJEE Main 2021

The image of an object placed in air formed by a convex refracting surface is at a distance of 10 m behind the surface. The image is real and is at

\frac{2^{rd}}{3}

of the distance of the object from the surface .The wavelength of light inside the surface is

\frac{2}{3}

times the wavelength in air. The radius of the curved surface is

\frac{x}{13}

m. the value of 'x' is__________.

Q192·PhysicsSingle correctJEE Main 2021

The thickness at the centre of a plano convex lens is 3 mm and the diameter is 6 cm. If the speed of light in the material of the lens is

2 \times 10^8

ms^{-1}

. The focal length of the lens is _____.

(A)0.30 cm
(B)15 cm
(C)1.5 cm
(D)30 cm

Q193·PhysicsNumericalJEE Main 2021

A deviation of 2° is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass are 0.02 and 0.03 respectively and refractive index for yellow light for these glasses are 1.5 and 1.6 respectively. The refracting angles for crown glass prism will be ________° (in degree) (Round off to the Nearest Integer)

Q194·PhysicsSingle correctJEE Main 2021

The angle of deviation through a prism is minimum when (A) Incident ray and emergent ray are symmetric to the prism (B) The refracted ray inside the prism becomes parallel to its base (C) Angle of incidence is equal to that of the angle of emergence (D) When angle of emergence is double the angle of incidence Choose the correct answer from the options given below :

(A)Statements (A), (B) and (C) are true
(B)Only statement (D) is true
(C)Only statements (A) and (B) are true
(D)Statements (B) and (C) are true

Q195·PhysicsSingle correctJEE Main 2021

The refractive index of a converging lens is 1.4. What will be the focal length of this lens if it is placed in a medium of same refractive index ? (Assume the radii of curvature of the faces of lens are R

_{1}

and R

_{2}

respectively)

(A)1
(B)Infinite
(C) $\frac{R_{1}R_{2}}{R_{1}-R_{2}}$
(D)Zero

Q196·PhysicsNumericalJEE Main 2021

A point source of light S, placed at a distance 60 cm infront of the centre of plane mirror of width 50 cm, hangs vertically on a wall. A man walks infront of the mirror along a line parallel to the mirror at a distance 1.2 m from it (see in the figure). The distance between the extreme points where he can see the image of the light source in the mirror is _______________cm

Q197·PhysicsSingle correctJEE Main 2021

Given below are two statements: One is labeled as Assertion A and the other is labeled as Reason R. Assertion A : For a simple microscope, the angular size of the object equals the angular size of the image. Reason R : Magnification is achieved as the small object can be kept much closer to the eye than 25 cm and hence it subtends a large angle. In the light of the above statements, choose the most appropriate answer from the options given below:

(A)Both A and R are true but R is NOT the correct explanationof A
(B)Both A and R are true and R is the correct explanation of A
(C)A is true but R is false
(D)A is false but R is true

Q198·PhysicsSingle correctJEE Main 2021

The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors

\vec{a}, \vec{b}

and

\vec{c}

respectively. Then choose the correct relation for these vectors.

(A) $\vec{b} = 2\vec{a} + \vec{c}$
(B) $\vec{b} = \vec{a} - \vec{c}$
(C) $\vec{b} = \vec{a} + 2\vec{c}$
(D) $\vec{b} = \vec{a} - 2\left(\vec{a}\cdot\vec{c}\right)\vec{c}$

Q199·PhysicsSingle correctJEE Main 2021

A short straight object of height 100 cm lies before the central axis of a spherical mirror whose focal length has absolute value |f| = 40 cm. The image of object produced by the mirror is of height 25 cm and has the same orientation of the object. One may conclude from the information :

(A)Image is real, same side of concave mirror.
(B)Image is virtual, opposite side of convex mirror.
(C)Image is virtual, opposite side of concave mirror.
(D)Image is real, same side of convex mirror.

Q200·PhysicsNumericalJEE Main 2021

The same size images are formed by a convex lens when the object is placed at 20 cm or at 10 cm from the lens. The focal length of convex lens is ________ cm.

Q201·PhysicsSingle correctJEE Main 2021

The focal length f is related to the radius of curvature r of the spherical convex mirror by -

(A) $f = r$
(B) $f = -\frac{1}{2}r$
(C) $f = +\frac{1}{2}r$
(D) $f = -r$

Q202·PhysicsMultiple correctJEE Advanced 2020

A beaker of radius

r

is filled with water (refractive index

\frac{4}{3}

) up to a height

H

as shown in the figure on the left. The beaker is kept on a horizontal table rotating with angular speed

\omega

. This makes the water surface curved so that the difference in the height of water level at the center and at the circumference of the beaker is

h

(

h \ll H, h \ll r

), as shown in the figure on the right. Take this surface to be approximately spherical with a radius of curvature

R

. Which of the following is/are correct? (g is the acceleration due to gravity)

(A) $R = \frac{h^2 + r^2}{2h}$
(B) $R = \frac{3r^2}{2h}$
(C)Apparent depth of the bottom of the beaker is close to $\frac{3H}{2}\left(1 + \frac{\omega^2 H}{2g}\right)^{-1}$
(D)Apparent depth of the bottom of the beaker is close to $\frac{3H}{4}\left(1 + \frac{\omega^2 H}{4g}\right)^{-1}$

Q203·PhysicsSingle correctJEE Main 2020

A point like object is placed at a distance of 1 m in front of convex lens of focal length 0.5 m. A plane mirror is placed at a distance of 2m behind the lens. The position and nature of the final image formed by the system is:

(A)2.6 m from the mirror, real
(B)1 m from the mirror, virtual
(C)1 m from the mirror, real
(D)2.6 m from the mirror, virtual

Q204·PhysicsSingle correctJEE Main 2020

A double convex lens has power P and same radii of curvature R of both the surfaces. The radius of curvature of a surface of a plano-convex lens made of the same material with power 1.5 P is

(A) $2R$
(B) $\frac{R}{2}$
(C) $\frac{3R}{2}$
(D) $\frac{R}{3}$

Q205·PhysicsSingle correctJEE Main 2020

For a concave lens of focal length f, the relation between object and image distances u and is

v

, respectively, from its pole can best be represented by (u -

v

is the reference line):

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q206·PhysicsNumericalJEE Main 2020

A prism of angle A = 1° has a refractive index

\mu = 1.5

. A good estimate for the minimum angle of deviation (in degrees) is close to N/10. Value of N is __________.

Q207·PhysicsNumericalJEE Main 2020

A compound microscope consists of an objective lens of focal length 1 cm and an eye piece of focal length 5 cm with a separation of 10 cm. The distance between an object and the objective lens, at which the strain on the eye is minimum is

\dfrac{n}{40}

cm. The value of n is ________.

Q208·PhysicsNumericalJEE Main 2020

The distance between an object and a screen is 100 cm. A lens can produce real image of the object on the screen for two different positions between the screen and the object. The distance between these two positions is 40 cm. If the power of the lens is close to

\left(\frac{N}{100}\right)

D where N is an integer, the value of N is ……….

Q209·PhysicsNumericalJEE Main 2020

In a compound microscope, the magnified virtual image is formed at a distance of 25 cm from the eye-piece. The focal length of its objective lens is 1 cm. If the magnification is 100 and the tube length of the microscope is 20 cm, then the focal length of the eye-piece lens (in cm) is _________.

Q210·PhysicsNumericalJEE Main 2020

When an object is kept at a distance of 30 cm from a concave mirror, the image is formed at a distance of 10 cm from the mirror. If the object is moved with a speed of 9 cm

s^{-1}

, the speed (in cm

s^{-1}

) with which image moves at that instant is _______________.

Q211·PhysicsNumericalJEE Main 2020

An observer can see through a small hole on the side of a jar (radius 15 cm) at a point at height of 15 cm from the bottom (see figure). The hole is at a height of 45 cm. When the jar is filled with a liquid up to a height of 30 cm the same observer can see the edge at the bottom of the jar. If the refractive index of the liquid is N / 100, where N is an integer, the value of N is __________.

Q212·PhysicsSingle correctJEE Main 2020

A vessel of depth 2h is half filled with a liquid of refractive index

2\sqrt{2}

and the upper half with another liquid of refractive index

\sqrt{2}

. The liquids are immiscible. The apparent depth of the inner surface of the bottom of vessel will be

(A) $\dfrac{h}{\sqrt{2}}$
(B) $\dfrac{h}{2(\sqrt{2}+1)}$
(C) $\dfrac{3}{4}h\sqrt{2}$
(D) $\dfrac{h}{3\sqrt{2}}$

Q213·PhysicsSingle correctJEE Main 2020

There is a small source of light at some depth below the surface of water (refractive index =

\frac{4}{3}

) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges out of surface is (nearly): [Use the fact that surface area of spherical cap of height h and radius of curvature r is 2πrh]

(A)21%
(B)17%
(C)50%
(D)34%

Q214·PhysicsNumericalJEE Main 2020

A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is 30 cm and the refractive index of the lens material is 1.5, then the focal length of the lens (in cm) is ___________.

Q215·PhysicsSingle correctJEE Main 2020

The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability

\dfrac{4}{3}

for this wavelength, will be

(A)60°
(B)15°
(C)45°
(D)30°

Q216·PhysicsSingle correctJEE Main 2020

The magnifying power of a telescope with tube length 60 cm is 5. What is the focal length of its eye piece?

(A)40 cm
(B)10 cm
(C)20 cm
(D)30 cm

Q217·PhysicsSingle correctJEE Main 2020

An object is gradually moving away from the focal point of a concave mirror along the axis of the mirror. The graphical representation of the magnitude of linear magnification (m) versus distance of the object from the mirror (x) is correctly given by (Graphs are drawn schematically and are not to scale)

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q218·PhysicsSingle correctJEE Main 2020

If we need a magnification of 375 from a compound microscope of tube length 150 mm and an objective of focal length 5 mm, the focal length of the eye piece should be close to

(A)22 mm
(B)33 m
(C)12 m
(D)2 mm

Q219·PhysicsSingle correctJEE Main 2020

A thin lens made of glass (refractive index = 1.5) of focal length f = 16 cm is immersed in a liquid of refractive index 1.42. If its focal length in liquid is f

_{\ell}

, then the ratio f

_{\ell}

/f is closest to the integer:

(A)17
(B)1
(C)9
(D)5

Q220·PhysicsNumericalJEE Advanced 2019

A planar structure of length L and width W is made of two different optical media of refractive indices

n_1

= 1.5 and

n_2

= 1.44 as shown in figure. If L >> W, a ray entering from end AB will emerge from end CD only if the total internal reflection condition is met inside the structure. For L = 9.6 m, if the incident angle θ is varied, the maximum time taken by a ray to exit the plane CD is t ×

10^{-9}

s, where t is ______. [Speed of light c = 3 ×

10^8

m/s]

Q221·PhysicsNumericalJEE Advanced 2019

A monochromatic light is incident from air on a refracting surface of prism of angle

75^\circ

and refractive index

n_0 = \sqrt{3}

. The other refracting surface of the prism is coated by a thin film of material of refractive index n as shown in figure. The light suffers total internal reflection at the coated prism surface for an incidence angle of

\theta \le 60^\circ

. The value of

n^2

is ________.

Q222·PhysicsMultiple correctJEE Advanced 2019

Three glass cylinders of equal height H = 30 cm and same refractive index n = 1.5 are placed on a horizontal surface as shown in figure. Cylinder I has a flat top, cylinder II has a convex top and cylinder III has a concave top. The radii of curvature of the two curved tops are same (R = 3m). If

H_1

,

H_2

and

H_3

are the apparent depths of a point X on the bottom of the three cylinders, respectively, the correct statement(s) is/are:

(A) $H_2 > H_1$
(B) $H_2 > H_3$
(C) $H_3 > H_1$
(D) $0.8$ cm $< (H_2 - H_1) < 0.9$ cm

Q223·PhysicsMultiple correctJEE Advanced 2019

A thin convex lens is made of two materials with refractive indices

n_1

and

n_2

, as shown in figure. The radius of curvature of the left and right spherical surfaces are equal. f is the focal length of the lens when

n_1 = n_2 = n

. The focal length is f + Δf when

n_1

= n and

n_2

= n + Δn. Assuming Δn << (n – 1) and 1 < n < 2. The correct statement(s) is/are.

(A) $\left|\frac{\Delta f}{f}\right| < \left|\frac{\Delta n}{n}\right|$
(B)If $\frac{\Delta n}{n} < 0$ then $\frac{\Delta f}{f} > 0$
(C)For n = 1.5, Δn = $10^{-3}$ and f = 20 cm, the value of |Δf| will be 0.02 cm (round off to $2^{nd}$ decimal place).
(D)The relation between $\frac{\Delta f}{f}$ and $\frac{\Delta n}{n}$ remains unchanged if both the convex surfaces are replaced by concave surfaces of the same radius of curvature.

Q224·PhysicsSingle correctJEE Main 2019

A concave mirror has radius of curvature of 40 cm. It is at the bottom of a glass that has water filled up to 5 cm (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance d from the surface of water. The value of d is close to : (Refractive index of water = 1.33)

(A)13.4 cm
(B)8.8 cm
(C)6.7 cm
(D)11.7 cm

Q225·PhysicsSingle correctJEE Main 2019

A transparent cube of side d, made of a material of refractive index

\mu_{2}

, is immersed in a liquid of refractive index

\mu_{1}(\mu_{1} < \mu_{2})

. A ray is incident on the face AB at an angle q(shown in the figure). Total internal reflection takes place at point E on the face BC. The q must satisfy :

(A) $\theta > \sin^{-1}\dfrac{\mu_{1}}{\mu_{2}}$
(B) $\theta > \sin^{-1}\sqrt{\dfrac{\mu_{2}^{2}}{\mu_{1}^{2}}-1}$
(C) $\theta < \sin^{-1}\dfrac{\mu_{1}}{\mu_{2}}$
(D) $\theta < \sin^{-1}\sqrt{\dfrac{\mu_{2}^{2}}{\mu_{1}^{2}}-1}$

Q226·PhysicsSingle correctJEE Main 2019

The graph shows how the magnification m produced by a thin lens varies with image distance v. What is the focal length of the lens used?

(A) $\dfrac{b^{2}}{ac}$
(B) $\dfrac{a}{c}$
(C) $\dfrac{b^{2}c}{a}$
(D) $\dfrac{b}{c}$

Q227·PhysicsSingle correctJEE Main 2019

A ray of light AO in vacuum is incident on a glass slab at angle 60° and refracted at angle 30° along OB as shown in the figure. The optical path length of light ray from A to B is :

(A) $2a + \dfrac{2b}{\sqrt{3}}$
(B) $2a + \dfrac{2b}{3}$
(C) $\dfrac{2\sqrt{3}}{a} + 2b$
(D) $2a + 2b$

Q228·PhysicsSingle correctJEE Main 2019

One plano-convex and one plano-concave lens of same radius of curvature 'R' but of different materials are joined side by side as shown in the figure. If the refractive index of the material of 1 is

\mu_{1}

and that of 2 is

\mu_{2}

, then the focal length of the combination is

(A) $\dfrac{R}{2(\mu_{1} - \mu_{2})}$
(B) $\dfrac{2R}{\mu_{1} - \mu_{2}}$
(C) $\dfrac{R}{\mu_{1} - \mu_{2}}$
(D) $\dfrac{R}{2 - (\mu_{1} - \mu_{2})}$

Q229·PhysicsSingle correctJEE Main 2019

A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is:

(A)0.16 m
(B)1.60 m
(C)0.24 m
(D)0.32 m

Q230·PhysicsSingle correctJEE Main 2019

A convex lens of focal length 20 cm produces images of the same magnification 2 when an object is kept at two distances

x_{1}

and

x_{2}

(x_{1} > x_{2})

from the lens. The ratio of

x_{1}

and

x_{2}

is:

(A)5 : 3
(B)2 : 1
(C)4 : 3
(D)3 : 1

Q231·PhysicsSingle correctJEE Main 2019

A convex lens (of focal length 20 cm) and a concave mirror, having their principal axes along the same lines, are kept 80 cm apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of 30 cm to the left o the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror, by itself would produce a virtual image would be:

(A)20 cm
(B)10 cm
(C)30 cm
(D)20 cm

Q232·PhysicsSingle correctJEE Main 2019

Formation of real image using a biconvex lens is shown below : If the whole set up is immersed in water without disturbing the object and the screen positions, what will one observe on the screen?

(A)Image disappears
(B)Magnified image
(C)Erect real image
(D)No change

Q233·PhysicsSingle correctJEE Main 2019

A point source of light, S is placed at a distance L in front of the centre of plane mirror of width d which is hanging vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror, at a distance 2 L as shown below. The distance over which the man can see the image of the light source in the mirror:

(A)d
(B)2d
(C)3d
(D) $\frac{d}{2}$

Q234·PhysicsSingle correctJEE Main 2019

A plano-convex lens (focal length f

_2

, refractive index

\mu_2

, radius of curvature R) fits exactly into a plano-concave lens (focal length f

_1

, refractive index

\mu_1

, radius of curvature R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be :

(A)f $_1$ − f $_2$
(B) $\frac{R}{\mu_2-\mu_1}$
(C) $\frac{2f_1f_2}{f_1+f_2}$
(D)f $_1$ + f $_2$

Q235·PhysicsSingle correctJEE Main 2019

What is the position and nature of image formed by lens combination shown in figure? (f

_{1}

, f

_{2}

are focal lengths)

(A)70 cm from point B at left; virtual
(B)40 cm from point B at right; real
(C) $\frac{20}{3}$ cm from point B at right; real
(D)70 cm from point B at right ; real

Q236·PhysicsSingle correctJEE Main 2019

The variation of refractive index of a crown glass thin prism with wavelength of the incident light is shown. Which of the following, graph is the correct one, if D

_m

is the angle of minimum deviation?

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q237·PhysicsSingle correctJEE Main 2019

A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractive index of the material of the prism is

\sqrt{3}

, then the angle of incidence

(A) $90^{\circ}$
(B) $30^{\circ}$
(C) $60^{\circ}$
(D) $45^{\circ}$

Q238·PhysicsSingle correctJEE Main 2019

An object is at a distance of 20 m from a convex lens of focal length 0.3 m. The lens forms an image of the object. If the object moves away from the lens at a speed of 5 m/s, the speed and direction of the image will be:

(A) $2.26 \times 10^{-3}$ m/s away from the lens
(B) $0.92 \times 10^{-3}$ m/s away from the lens
(C) $3.22 \times 10^{-3}$ m/s towards the lens
(D) $1.16 \times 10^{-3}$ m/s towards the lens

Q239·PhysicsSingle correctJEE Main 2019

Two plane mirrors are inclined to each other such that a ray of light incident to the first mirror (M

_1

) and parallel to the second mirror (M

_2

) is finally reflected from the second mirror (M

_2

) parallel to the first mirror (M

_1

). The angle between the two mirrors will be:

(A)45°
(B)60°
(C)75°
(D)90°

Q240·PhysicsSingle correctJEE Main 2019

A convex lens is put 10 cm from a light source and it makes a sharp image on a screen, kept 10 cm from the lens. Now a glass block (refractive index 1.5) of 1.5 cm thickness is placed in contact with the light source. To get the sharp image again, the screen is shifted by a distance d. Then d is:

(A)1.1 cm away fro the lens
(B)0
(C)0.55 cm towards the lens
(D)0.55 cm away from the lens

Q241·PhysicsNumericalJEE Advanced 2018

Sunlight of intensity

1.3\ \mathrm{kWm}^{-2}

is incident normally on a thin convex lens of focal length

20\ cm

. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light, in

kW\ m^{-2}

, at a distance

22\ cm

from the lens on the other side is __________.

Q242·PhysicsMultiple correctJEE Advanced 2018

A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length

f

, as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are not to scale.)

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q243·PhysicsMultiple correctJEE Advanced 2017

For an isosceles prism of angle A and refractive index

\mu

, it is found that the angle of minimum deviation

\delta_{m}

= A. Which of the following options is/are correct?

(A)At minimum deviation, the incident angle $i_{1}$ and the refracting angle $r_{1}$ at the first refracting surface are related by $r_{1} = (i_{1}/2)$ .
(B)For this prism the refractive index $\mu$ and the angle of prism A are related as $A = \frac{1}{2}\cos^{-1}(\mu/2)$ .
(C)For this prism, the emergent ray at the second surface will be tangential to the surface when the angle of incidence at the first surface is $i_{1} = \sin^{-1}\left[\sin A\sqrt{4\cos^{2}\frac{A}{2}-1}-\cos A\right]$ .
(D)For the angle of incidence $i_{1}$ = A, the ray inside the prism is parallel to the base of the prism.

Q244·PhysicsIntegerJEE Advanced 2017

A monochromatic light is travelling in a medium of refractive index n = 1.6. It enters a stack of glass layers from the bottom side at an angle

\theta

= 30

^{\circ}

. The interfaces of the glass layers are parallel to each other. The refractive indices of different glass layers are monotonically decreasing as

n_{m}

= n

-

m

\Delta

n, where

n_{m}

is the refractive index of the

m^{th}

slab and

\Delta

n = 0.1 (see the figure). The ray is refracted out parallel to the interface between the (m

-

1)

^{th}

and

m^{th}

slabs from the right side of the stack. What is the value of m?

Q245·PhysicsSingle correctJEE Advanced 2016

A parallel beam of light is incident from air at an angle

\alpha

on the side PQ of a right angled triangular prism of refractive index

n = \sqrt{2}

. Light undergoes total internal reflection in the prism at the face PR when

\alpha

has a minimum value of

45^{0}

. The angle

\theta

of the prism is

(A) $15^{0}$
(B) $22.5^{0}$
(C) $30^{0}$
(D) $45^{0}$

Q246·PhysicsMultiple correctJEE Advanced 2016

A plano-convex lens is made of a material of refractive index n. When a small object is placed 30 cm away in front of the curved surface of the lens, an image of double the size of the object is produced. Due to reflection from the convex surface of the lens, another faint image is observed at a distance of 10 cm away from the lens. Which of the following statement(s) is(are) true?

(A)The refractive index of the lens is 2.5
(B)The radius of curvature of the convex surface is 45 cm
(C)The faint image is erect and real
(D)The focal length of the lens is 20 cm

Q247·PhysicsSingle correctJEE Advanced 2016

A small object is placed 50 cm to the left of a thin convex lens of focal length 30 cm. A convex spherical mirror of radius of curvature 100 cm is placed to the right of the lens at a distance of 50 cm. The mirror is tilted such that the axis of the mirror is at an angle

\theta = 30^{0}

to the axis of the lens, as shown in the figure. If the origin of the coordinate system is taken to be at the centre of the lens, the coordinates (in cm) of the point (x, y) at which the image is formed are

(A) $(25,\ 25\sqrt{3})$
(B) $(125/3,\ 25/\sqrt{3})$
(C) $(50 - 25\sqrt{3},\ 25)$
(D) $(0,\ 0)$

Q248·PhysicsMultiple correctJEE Advanced 2016

A transparent slab of thickness

d

has a refractive index

n(z)

that increases with

z

. Here

z

is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices

n_1

and

n_2

(

> n_1

), as shown in the figure. A ray of light is incident with angle

\theta_i

from medium 1 and emerges in medium 2 with refraction angle

\theta_f

with a lateral displacement

l

. Which of the following statement (s) is (are) true?

(A) $n_1 \sin\theta_i = n_2 \sin\theta_f$
(B) $n_1 \sin\theta_i = (n_2 - n_1)\sin\theta_f$
(C) $l$ is independent of $n_2$
(D) $l$ is dependent on $n(z)$

Q249·PhysicsIntegerJEE Advanced 2015

A monochromatic beam of light is incident at

60^{0}

on one face of an equilateral prism of refractive index n and emerges from the opposite face making an angle

\theta(n)

with the normal (see the figure). For

n = \sqrt{3}

the value of

\theta

is

60^{0}

and

\dfrac{d\theta}{dn} = m

. The value of m is

Q250·PhysicsMultiple correctJEE Advanced 2015

Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index

n_{1}

surrounded by a medium of lower refractive index

n_{2}

. The light guidance in the structure takes place due to successive total internal reflections at the interface of the media

n_{1}

and

n_{2}

as shown in the figure. All rays with the angle of incidence

i

less than a particular value

i_{m}

are confined in the medium of refractive index

n_{1}

. The numerical aperture (NA) of the structure is defined as

\sin i_{m}

. For two structures namely

S_{1}

with

n_{1} = \sqrt{45}/4

and

n_{2} = 3/2

, and

S_{2}

with

n_{1} = 8/5

and

n_{2} = 7/5

and taking the refractive index of water to be 4/3 and that of air to be 1, the correct option(s) is(are)

(A)NA of $S_{1}$ immersed in water is the same as that of $S_{2}$ immersed in a liquid of refractive index $\dfrac{16}{3\sqrt{15}}$
(B)NA of $S_{1}$ immersed in liquid of refractive index $\dfrac{6}{\sqrt{15}}$ is the same as that of $S_{2}$ immersed in water
(C)NA of $S_{1}$ placed in air is the same as that of $S_{2}$ immersed in liquid of refractive index $\dfrac{4}{\sqrt{15}}$
(D)NA of $S_{1}$ placed in air is the same as that of $S_{2}$ placed in water

Q251·PhysicsMultiple correctJEE Advanced 2015

Two identical glass rods

S_{1}

and

S_{2}

(refractive index = 1.5) have one convex end of radius of curvature 10 cm. They are placed with the curved surfaces at a distance

d

as shown in the figure, with their axes (shown by the dashed line) aligned. When a point source of light P is placed inside rod

S_{1}

on its axis at a distance of 50 cm from the curved face, the light rays emanating from it are found to be parallel to the axis inside

S_{2}

. The distance

d

is

(A)60 cm
(B)70 cm
(C)80 cm
(D)90 cm

Q252·PhysicsIntegerJEE Advanced 2015

Consider a concave mirror and a convex lens (refractive index = 1.5) of focal length 10 cm each, separated by a distance of 50 cm in air (refractive index = 1) as shown in the figure. An object is placed at a distance of 15 cm from the mirror. Its erect image formed by this combination has magnification

M_{1}

. When the set-up is kept in a medium of refractive index

7/6

, the magnification becomes

M_{2}

. The magnitude

\left|\dfrac{M_{2}}{M_{1}}\right|

is

Q253·PhysicsMultiple correctJEE Advanced 2015

Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index

n_{1}

surrounded by a medium of lower refractive index

n_{2}

. The light guidance in the structure takes place due to successive total internal reflections at the interface of the media

n_{1}

and

n_{2}

as shown in the figure. All rays with the angle of incidence

i

less than a particular value

i_{m}

are confined in the medium of refractive index

n_{1}

. The numerical aperture (NA) of the structure is defined as

\sin i_{m}

. If two structures of same cross-sectional area, but different numerical apertures

NA_{1}

and

NA_{2}

(NA_{2} < NA_{1})

are joined longitudinally, the numerical aperture of the combined structure is

(A) $\dfrac{NA_{1}NA_{2}}{NA_{1} + NA_{2}}$
(B) $NA_{1} + NA_{2}$
(C) $NA_{1}$
(D) $NA_{2}$

Q254·PhysicsMultiple correctJEE Advanced 2014

A transparent thin film of uniform thickness and refractive index

n_1 = 1.4

is coated on the convex spherical surface of radius

R

at one end of a long solid glass cylinder of refractive index

n_2 = 1.5

, as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance

f_1

from the film, while rays of light traversing from glass to air get focused at distance

f_2

from the film. Then

(A) $|f_1| = 3R$
(B) $|f_1| = 2.8R$
(C) $|f_2| = 2R$
(D) $|f_2| = 1.4R$

Q255·PhysicsSingle correctJEE Advanced 2014

Four combinations of two thin lenses are given in List I. The radius of curvature of all curved surfaces is

r

and the refractive index of all the lenses is 1.5. Match lens combinations in List I with their focal length in List II and select the correct answer using the code given below the lists.

List I	List II
P.see figure	1. $2r$
Q.see figure	2. $r/2$
R.see figure	3. $-r$
S.see figure	4. $r$

(A)P-1, Q-2, R-3, S-4
(B)P-2, Q-4, R-3, S-1
(C)P-4, Q-1, R-2, S-3
(D)P-2, Q-1, R-3, S-4

Q256·PhysicsSingle correctJEE Advanced 2014

A point source S is placed at the bottom of a transparent block of height 10 mm and refractive index 2.72. It is immersed in a lower refractive index liquid as shown in the figure. It is found that the light emerging from the block to the liquid forms a circular bright spot of diameter 11.54 mm on the top of the block. The refractive index of the liquid is

(A)1.21
(B)1.30
(C)1.36
(D)1.42

Q257·PhysicsSingle correctJEE Advanced 2013

A ray of light travelling in the direction

\frac{1}{2}(\hat{i}+\sqrt{3}\hat{j})

is incident on a plane mirror. After reflection, it travels along the direction

\frac{1}{2}(\hat{i}-\sqrt{3}\hat{j})

. The angle of incidence is

(A)30°
(B)45°
(C)60°
(D)75°

Q258·PhysicsSingle correctJEE Advanced 2013

A right angled prism of refractive index

\mu_{1}

is placed in a rectangular block of refractive index

\mu_{2}

, which is surrounded by a medium of refractive index

\mu_{3}

, as shown in the figure. A ray of light 'e' enters the rectangular block at normal incidence. Depending upon the relationships between

\mu_{1}

,

\mu_{2}

and

\mu_{3}

, it takes one of the four possible paths 'ef', 'eg', 'eh', or 'ei'. Match the paths in List I with conditions of refractive indices in List II and select the correct answer using the codes given below the lists:

List I	List II
P. $e \to f$	1. $\mu_{1} > \sqrt{2}\,\mu_{2}$
Q. $e \to g$	2. $\mu_{2} > \mu_{1}$ and $\mu_{2} > \mu_{3}$
R. $e \to h$	3. $\mu_{1} = \mu_{2}$
S. $e \to i$	4. $\mu_{2} < \mu_{1} < \sqrt{2}\,\mu_{2}$ and $\mu_{2} > \mu_{3}$

(A)P-2, Q-3, R-1, S-4
(B)P-1, Q-2, R-4, S-3
(C)P-4, Q-1, R-2, S-3
(D)P-2, Q-3, R-4, S-1

Q259·PhysicsSingle correctJEE Advanced 2013

The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is

\frac{2}{3}

times the wavelength in free space. The radius of the curved surface of the lens is

(A)1 m
(B)2 m
(C)3 m
(D)4 m

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