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Optics

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JEE Advanced 1991

LEVELJEE Advanced

Two parallel beams of light $P$ and $Q$ (separation $d$ ) containing radiations of wavelengths $4000 \overset{˚}{A}$ and $5000 \overset{˚}{A}$ (which are mutually coherent in each wavelength separately) are incident normally on a prism as shown in figure. The refractive index of the prism as a function of wavelength is given by the relation, $μ (λ) = 1.20 + \frac{b}{λ ^{2}}$ where $λ$ is in $\overset{˚}{A}$ and $b$ is positive constant. The value of $b$ is such that the condition for total reflection at the face $A C$ is just satisfied for one wavelength and is not satisfied for the other. (a) Find the value of $b$ . (b) Find the deviation of the beams transmitted through the face $A C$ . (c) A convergent lens is used to bring these transmitted beams into focus. If the intensities of the upper and the lower beams immediately after transmission from the face $A C$ , are $4 I$ and $I$ respectively, find the resultant intensity at the focus.

JEE Advanced 1998

LEVELJEE Advanced

A coherent parallel beam of microwaves of wavelength $λ = 0.5 mm$ falls on a Young's double slit apparatus. The separation between the slits is $1.0 mm$ . The intensity of microwaves is measured on a screen placed parallel to the plane of the slits at a distance of $1.0 m$ from it as shown in the figure. (a) If the incident beam falls normally on the double slit apparatus, find the $y$ -coordinates of all the interference minima on the screen. (b) If the incident beam makes an angle of $3 0^{\circ}$ with the $x$ -axis (as in the dotted arrow shown in figure), find the $y$ -coordinates of the first minima on either side of the central maximum.

JEE Advanced 1999

LEVELJEE Advanced

The Young's double slit experiment is done in a medium of refractive index $4/3$ . A light of $600 nm$ wavelength is falling on the slits having $0.45 mm$ separation. The lower slit $S_{2}$ is covered by a thin glass sheet of thickness $10.4 \mu m$ and refractive index $1.5$ . The interference pattern is observed on a screen placed $1.5 m$ from the slits as shown in the figure. (a) Find the location of central maximum (bright fringe with zero path difference) on the $y$ -axis. (b) Find the light intensity of point $O$ relative to the maximum fringe intensity. (c) Now, if $600 nm$ light is replaced by white light of range $400$ to $700 nm$ , find the wavelengths of the light that form maxima exactly at point $O$ . (All wavelengths in the problem are for the given medium of refractive index $4/3$ . Ignore dispersion)

JEE Advanced 2001

LEVELJEE Advanced

A vessel $A B C D$ of 10 cm width has two small slits $S_{1}$ and $S_{2}$ sealed with identical glass plates of equal thickness. The distance between the slits is 0.8 mm. $P O Q$ is the line perpendicular to the plane $A B$ and passing through $O$ , the middle point of $S_{1}$ and $S_{2}$ . A monochromatic light source is kept at $S$ , 40 cm below $P$ and 2 m from the vessel, to illuminate the slits as shown in the figure alongside. Calculate the position of the central bright fringe on the other wall $C D$ with respect to the line $O Q$ . Now, a liquid is poured into the vessel and filled upto $O Q$ . The central bright fringe is found to be at $Q$ . Calculate the refractive index of the liquid.

JEE Advanced 2017

LEVELJEE Advanced

For an isosceles prism of angle $A$ and refractive index $μ$ , it is found that the angle of minimum deviation $δ_{m} = A$ . Which of the following options is/are correct?

* Multiple Correct Options

(A)

For the angle of incidence

i_{1} = A

, the ray inside the prism is parallel to the base of the prism

(B)

At minimum deviation, the incident angle

i_{1}

and the refracting angle

r_{1}

at the first refracting surface are related by

r_{1} = (\frac{i _{1}}{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} [sin A 4 cos^{2} \frac{A}{2} - 1 - cos A]

(D)

For this prism, the refractive index

μ

and the angle prism

A

are related as

A = \frac{1}{2} cos^{- 1} (\frac{μ}{2})

JEE Advanced 2015

LEVELJEE Advanced

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 $\frac{M _{2}}{M _{1}}$ is

JEE Advanced 2017

LEVELJEE Advanced

Two coherent monochromatic point sources $S_{1}$ and $S_{2}$ of wavelength $λ = 600 nm$ are placed symmetrically on either side of the centre of the circle as shown. The sources are separated by a distance $d = 1.8 mm$ . This arrangement produces interference fringes visible as alternate bright and dark spots on the circumference of the circle. The angular separation between two consecutive bright spots is $Δ θ$ . Which of the following options is/are correct?

* Multiple Correct Options

(A)

The angular separation between two consecutive bright spots decreases as we move from

P_{1}

P_{2}

along the first quadrant

(B)

A dark spot will be formed at the point

P_{2}

(C)

The total number of fringes produced between

P_{1}

and

P_{2}

in the first quadrant is close to 3000

(D)

P_{2}

the order of the fringe will be maximum

JEE Advanced 1997

LEVELJEE Advanced

In a Young's experiment, the upper slit is covered by a thin glass plate of refractive index 1.4, while the lower slit is covered by another glass plate, having the same thickness as the first one but having refractive index 1.7. Interference pattern is observed using light of wavelength $5400 \overset{˚}{A}$ . It is found that the point $P$ on the screen, where the central maximum ( $n = 0$ ) fall before the glass plates were inserted, now has $3/4$ the original intensity. It is further observed that what used to be the fifth maximum earlier lies below the point $P$ while the sixth minima lies above $P$ . Calculate the thickness of glass plate. (Absorption of light by glass plate may be neglected).

JEE Advanced 1993

LEVELJEE Advanced

In given figure, $S$ is a monochromatic point source emitting light of wavelength $λ = 500 nm$ . A thin lens of circular shape and focal length $0.10 m$ is cut into two identical halves $L_{1}$ and $L_{2}$ by a plane passing through a diameter. The two halves are placed symmetrically about the central axis $S O$ with a gap of $0.5 mm$ . The distance along the axis from $S$ to $L_{1}$ and $L_{2}$ is $0.15 m$ while that from $L_{1}$ and $L_{2}$ to $O$ is $1.30 m$ . The screen at $O$ is normal to $S O$ . (a) If the third intensity maximum occurs at the point $A$ on the screen, find the distance $O A$ . (b) If the gap between $L_{1}$ and $L_{2}$ is reduced from its original value of $0.5 mm$ , will the distance $O A$ increase, decrease, or remain the same.

JEE Advanced 2000

LEVELJEE Advanced

A convex lens of focal length 15 cm and a concave mirror of focal length 30 cm are kept with their optic axis $P Q$ and $R S$ parallel but separated in vertical direction by 0.6 cm as shown. The distance between the lens and mirror is 30 cm. An upright object $A B$ of height 1.2 cm is placed on the optic axis $P Q$ of the lens at a distance of 20 cm from the lens. If $A^{'} B^{'}$ is the image after refraction from the lens and the reflection from the mirror, find the distance of $A^{'} B^{'}$ from the pole of the mirror and obtain its magnification. Also locate positions of $A^{'}$ and $B^{'}$ with respect to the optic axis $R S$ .

JEE Advanced 1995

LEVELJEE Advanced

A ray of light travelling in air is incident at grazing angle (Incident angle = $9 0^{\circ}$ ) on a long rectangular slab of a transparent medium of thickness $t = 1.0$ m. The point of incidence is the origin $A (0, 0)$ . The medium has a variable index of refraction $n (y)$ given by $n (y) = [k y^{3/2} + 1]^{1/2}$ where $k = 1.0 (m)^{- 3/2}$ . The refractive index of air is 1.0. (1995) (a) Obtain a relation between the slope of the trajectory of the ray at a point $B (x, y)$ in the medium and the incident angle at that point. (b) Obtain an equation for the trajectory $y (x)$ of the ray in the medium. (c) Determine the coordinates $(x_{1}, y_{1})$ of the point $P$ , where the ray intersects the upper surface of the slab-air boundary. (d) Indicate the path of the ray subsequently.

JEE Advanced 2010

LEVELJEE Advanced

A ray $O P$ of monochromatic light is incident on the face $A B$ of prism $A B C D$ near vertex $B$ at an incident angle of $6 0^{\circ}$ (see figure). If the refractive index of the material of the prism is $3$ , which of the following is (are) correct?

* Multiple Correct Options

(A)

The ray gets totally internally reflected at face

C D

(B)

The ray comes out through face

A D

(C)

The angle between the incident ray and the emergent ray is

9 0^{\circ}

(D)

The angle between the incident ray and the emergent ray is

12 0^{\circ}

JEE Advanced 2015

LEVELJEE Advanced

A monochromatic beam of light is incident at $6 0^{\circ}$ on one face of an equilateral prism of refractive index $n$ and emerges from the opposite face making an angle $θ (n)$ with the normal (see figure). For $n = 3$ the value of $θ$ is $6 0^{\circ}$ and $\frac{d θ}{d n} = m$ . The value of $m$ is

JEE Advanced 1997

LEVELJEE Advanced

A thin equiconvex lens of glass of refractive index $μ = 3/2$ and of focal length $0.3 m$ in air is sealed into an opening at one end of a tank filled with water $μ = 4/3$ . On the opposite side of the lens, a mirror is placed inside the tank on the tank wall perpendicular to the lens axis, as shown in figure. The separation between the lens and the mirror is $0.8 m$ . A small object is placed outside the tank in front of lens. Find the position (relative to the lens) of the image of the object formed by the system

JEE Advanced 2009

LEVELJEE Advanced

Column I shows four situations of standard Young's double slit arrangement with the screen placed far away from the slits $S_{1}$ and $S_{2}$ . In each of these cases $S_{1} P_{0} = S_{2} P_{0}, S_{1} P_{1} - S_{2} P_{1} = \frac{λ}{4}$ and $S_{1} P_{2} - S_{2} P_{2} = \frac{λ}{3}$ , where $λ$ is the wavelength of the light used. In the cases B, C and D, a transparent sheet of refractive index $μ$ and thickness $t$ is pasted on slit $S_{2}$ . The thickness of the sheets are different in different cases. The phase difference between the light waves reaching a point $P$ on the screen from the two slits is denoted by $δ (P)$ and the intensity by $I (P)$ . Match each situation given in Column I with the statement(s) in Column II valid for that situation.

List-I

(P)

(Q)

(μ - 1) t = \frac{λ}{4}

(R)

(μ - 1) t = \frac{λ}{2}

(S)

(μ - 1) t = \frac{3 λ}{4}

List-II

(1)

δ (P_{0}) = 0

(2)

δ (P_{1}) = 0

(3)

I (P_{1}) = 0

(4)

I (P_{0}) > I (P_{1})

(5)

I (P_{2}) > I (P_{1})

JEE Advanced 2010

LEVELJEE Advanced

Two transparent media of refractive indices $μ_{1}$ and $μ_{3}$ have a solid lens shaped transparent material of refractive index $μ_{2}$ between them as shown in figures in Column II. A ray traversing these media is also shown in the figures. In Column I different relationships between $μ_{1}, μ_{2}$ and $μ_{3}$ are given. Match them to the ray diagram shown in Column II.

List-I

(P)

μ_{1} < μ_{2}

(Q)

μ_{1} > μ_{2}

(R)

μ_{2} = μ_{3}

(S)

μ_{2} > μ_{3}

List-II

Monochromatic light is incident on a plane interface $A B$ between two media of refractive indices $n_{1}$ and $n_{2}$ ( $n_{2} > n_{1}$ ) at an angle of incidence $θ$ as shown in the figure. The angle $θ$ is infinitesimally greater than the critical angle for the two media so that total internal reflection takes place. Now if a transparent slab $D E F G$ of uniform thickness and of refractive index $n_{3}$ is introduced on the interface (as shown in the figure), show that for any value of $n_{3}$ all light will ultimately be reflected back again into medium II. Consider separately the cases : (a) $n_{3} < n_{1}$ and (b) $n_{3} > n_{1}$

JEE Advanced 2025

LEVELJEE Advanced

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:

* Multiple Correct Options

(A)

4 f + (1 - \frac{1}{n _{0}}) t

(B)

2 f + (1 - \frac{1}{n _{0}}) t

(C)

4 f + (n_{0} - 1) t

(D)

2 f + (n_{0} - 1) t

JEE Advanced 2020

LEVELJEE Advanced

A large square container with thin transparent vertical walls and filled with water (refractive index 4/3) is kept on a horizontal table. A student holds a thin straight wire vertically inside the water 12 cm from one of its corners, as shown schematically in the figure. Looking at the wire from this corner, another student sees two images of the wire, located symmetrically on each side of the line of sight as shown. The separation (in cm) between these images is_________.

JEE Advanced 2016

LEVELJEE Advanced

A small object is placed 50 cm to the left of 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 $θ = 3 0^{\circ}$ 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, 253)

(B)

(\frac{125}{3}, \frac{25}{3})

(C)

(50 - 253, 25)

(D)

(0, 0)

Micro-Topic Strategy Matrix

Plane Mirror

Spherical Mirror

Refraction and Total Internal Reflection

Refraction at Spherical Surface

Lens

Refraction and Dispersion through Prism

Optical Instruments

Huygens' Principle and Wavefronts

Interference and Young's Double-Slit Experiment

Diffraction due to Single Slit

Polarization

Chapter Elite-20 Challenge Zone

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } For an isosceles prism of angle A and refractive index μ, it is found that the angle of minimum deviation δm​=A. Which of the following options is/are correct?

List-I

List-II

List-I

List-II

For an isosceles prism of angle $A$ and refractive index $μ$ , it is found that the angle of minimum deviation $δ_{m} = A$ . Which of the following options is/are correct?