Refraction at Spherical Surface

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JEE Advanced 1984

LEVELJEE Advanced

A plano-convex lens has a thickness of $4 cm$ . When placed on a horizontal table, with the curved surface in contact with it, the apparent depth of the bottom most point of the lens is found to be $3 cm$ . If the lens is inverted such that the plane face is in contact with the table, the apparent depth of the centre of the plane face is found to be $25/8 cm$ . Find the focal length of the lens. Assume thickness to be negligible while finding its focal length.

LEVELJEE Advanced

In the figure, light is incident on a thin lens as shown. The radius of curvature for both the surfaces is $R$ . Determine the focal length of this system.

JEE Advanced 2011

LEVELJEE Advanced

Water (with refractive index = 4/3) in a tank is 18 cm deep. Oil of refractive index 7/4 lies on water making a convex surface of radius of curvature R = 6 cm as shown. Consider oil to act as a thin lens. An object S is placed 24 cm above water surface. The location of its image is at x cm above the bottom of the tank. Then x is.

LEVELJEE Advanced

A point object is placed at a distance of 20 cm from a thin plano-convex lens of focal length 15 cm. The plane surface of the lens is now silvered. The image created by the system is at

(A)

60 cm to the left of the system

(B)

60 cm to the right of the system

(C)

12 cm to the left of the system

(D)

12 cm to the right of the system

JEE Main 2004

LEVELJEE Main

A point object is placed at the centre of a glass sphere of radius $6 cm$ and refractive index $1.5$ . The distance of the virtual image from the surface of the sphere is

(A)

2 cm

(B)

4 cm

(C)

6 cm

(D)

12 cm

LEVELJEE Advanced

A quarter cylinder of radius $R$ and refractive index $1.5$ is placed on a table. A point object $P$ is kept at a distance of $m R$ from it. Find the value of $m$ for which a ray from $P$ will emerge parallel to the table as shown in figure.

LEVELJEE Main

A slab of material of refractive index 2 shown in figure has a curved surface APB of radius of curvature 10 cm and a plane surface CD. On the left of APB is air and on the right of CD is water with refractive indices as given in the figure. An object O is placed at a distance of 15 cm from the pole P as shown. The distance of the final image of O from P, as viewed from the left is ……

LEVELJEE Main

Which one of the following spherical lenses does not exhibit dispersion? The radii of curvature of the surfaces of the lenses are as given in the diagrams

A plano-convex lens is made of 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?

* Multiple Correct Options

(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

JEE Advanced 1988

LEVELJEE Advanced

A parallel beam of light travelling in water (refractive index = 4/3) is refracted by a spherical air bubble of radius 2 mm situated in water. Assuming the light rays to be paraxial. (a) Find the position of the image due to refraction at the first surface and the position of the final image. (b) Draw a ray diagram showing the positions of both the images.

JEE Advanced 2015

LEVELJEE Advanced

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

The convex surface of a thin concavo-convex lens of glass of refractive index 1.5 has a radius of curvature 20 cm. The concave surface has a radius of curvature 60 cm. The convex side is silvered and placed on a horizontal surface. (a) Where should a pin be placed on the optic axis such that its image is formed at the same place? (b) If the concave part is filled with water of refractive index 4/3, find the distance through which the pin should be moved, so that the image of the pin again coincides with the pin.

LEVELJEE Main

A spherical surface of radius of curvature $R$ , separates air (refractive index $1.0$ ) from glass (refractive index $1.5$ ). The centre of curvature is in the glass. A point object $P$ placed in air is found to have a real image $Q$ in the glass. The line $P Q$ cuts the surface at a point $O$ and $P O = O Q$ . The distance $P O$ is equal to

(A)

5 R

(B)

3 R

(C)

2 R

(D)

1.5 R

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 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

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

* Multiple Correct Options

(A)

∣ f_{1} ∣ = 3 R

(B)

∣ f_{1} ∣ = 2.8 R

(C)

∣ f_{2} ∣ = 2 R

(D)

∣ f_{2} ∣ = 1.4 R

JEE Advanced 2004

LEVELJEE Advanced

Figure shows an irregular block of material of refractive index $2$ . A ray of light strikes the face $A B$ as shown in the figure. After refraction it is incident on a spherical surface $C D$ of radius of curvature $0.4 m$ and enters a medium of refractive index $1.514$ to meet $P Q$ at $E$ . Find the distance $O E$ upto two places of decimal.

JEE Advanced 2024

LEVELJEE Advanced

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?

* Multiple Correct Options

(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.

JEE Advanced 2024

LEVELJEE Advanced

A light ray is incident on the surface of a sphere of refractive index $n$ at an angle of incidence $θ_{0}$ . The ray partially refracts into the sphere with angle of refraction $ϕ_{0}$ 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 $α$ . Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

List-I

(P)

n = 2

and

α = 18 0^{\circ}

, then all the possible values of

θ_{0}

will be

(Q)

n = 3

and

α = 18 0^{\circ}

, then all the possible values of

θ_{0}

will be

(R)

n = 3

and

α = 18 0^{\circ}

, then all the possible values of

ϕ_{0}

will be

(S)

n = 2

and

θ_{0} = 4 5^{\circ}

, then all the possible values of

α

will be

List-II

(1)

3 0^{\circ}

and

0^{\circ}

(2)

6 0^{\circ}

and

0^{\circ}

(3)

4 5^{\circ}

and

0^{\circ}

(4)

15 0^{\circ}

(5)

0^{\circ}

JEE Advanced 2020

LEVELJEE Advanced

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 $ω$ . 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 $h$ ( $h ≪ H$ , $h ≪ r$ ), 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)

* Multiple Correct Options

(A)

R = \frac{h ^{2} + r ^{2}}{2 h}

(B)

R = \frac{3 r ^{2}}{2 h}

(C)

Apparent depth of the bottom of the beaker is close to

\frac{3 H}{2} (1 + \frac{ω ^{2} H}{2 g})^{- 1}

(D)

Apparent depth of the bottom of the beaker is close to

\frac{3 H}{4} (1 + \frac{ω ^{2} H}{4 g})^{- 1}

JEE Main 2020

LEVELJEE Main

A light ray enters a solid glass sphere of refractive index $μ = 3$ at an angle of incidence $6 0^{\circ}$ . The ray is both reflected and refracted at the farther surface of the sphere. The angle (in degree) between the reflected and refracted rays at this surface is ……… .

JEE Main 2019

LEVELJEE Advanced

A thin convex lens $L$ (refractive index = 1.5) is placed on a plane mirror $M$ . When a pin is placed at $A$ , such that $O A = 18$ cm, its real inverted image is formed at $A$ itself, as shown in figure. When a liquid of refractive index $μ_{l}$ is put between the lens and the mirror, the pin has to be moved to $A^{'}$ , such that $O A^{'} = 27$ cm, to get its inverted real image at $A^{'}$ itself. The value of $μ_{l}$ will be

(A)

3

(B)

2

(C)

\frac{4}{3}

(D)

\frac{3}{2}

JEE Main 2021

LEVELJEE Main

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)

55.44 cm

(B)

9.52 cm

(C)

18.23 cm

(D)

37.58 cm

JEE Main 2021

LEVELJEE Advanced

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 $\frac{2}{3}$ 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 ............... .

JEE Main 2019

LEVELJEE Main

The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of cornea ( $7.8 mm$ ). This surface separates two media of refractive indices $1$ and $1.34$ . Calculate the distance from the refracting surface at which a parallel beam of light will come to focus.

(A)

4.0 cm

(B)

2 cm

(C)

3.1 cm

(D)

1 cm

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } In the figure, light is incident on a thin lens as shown. The radius of curvature for both the surfaces is R. Determine the focal length of this system.

A point object is placed at a distance of 20 cm from a thin plano-convex lens of focal length 15 cm. The plane surface of the lens is now silvered. The image created by the system is at

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A point object is placed at the centre of a glass sphere of radius 6 cm and refractive index 1.5. The distance of the virtual image from the surface of the sphere is

Which one of the following spherical lenses does not exhibit dispersion? The radii of curvature of the surfaces of the lenses are as given in the diagrams

List-I

List-II

List-I

List-II

In the figure, light is incident on a thin lens as shown. The radius of curvature for both the surfaces is $R$ . Determine the focal length of this system.

A point object is placed at the centre of a glass sphere of radius $6 cm$ and refractive index $1.5$ . The distance of the virtual image from the surface of the sphere is