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

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 planoconcave 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 $\_\_\_\_$

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

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 +5 D as $(25,96),(30,62),(35,37),(45,35)$ and $(50,32)$ respectively. Identify correct statement

The exit surface of a prism with refractive index $n$ is coated with a material having refractive index $\frac{n}{2}$. When this prism is set for minimum angle of deviation, it exactly meets the condition of critical angle. The prism angle is $\_\_\_\_$ .

An unpolarised light is incident at an interface of two dielectric media having refractive indices of 2 (incident medium) and $2 \sqrt{3}$ (medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is $\_\_\_\_$

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 thin prism with angle $5^{\circ}$ 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 $\_\_\_\_$ .

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 $2.4 \times 10^8 \mathrm{~m} / \mathrm{s}$ and $2.7 \times 10^8 \mathrm{~m} / \mathrm{s}$, respectively, then the value of critical angle is :

In parallax method for the determination of focal length of a concave mirror, the object should always be placed:

A thin convex lens of focal length 5 cm and a thin concave lens of focal length 4 cm are combined together (without any gap) and this combination has magnification $m_1$ when an object is placed 10 cm before the convex lens. Keeping the positions of convex lens and object undisturbed a gap of 1 cm is introduced between the lenses by moving the concave lens away, which lead to a change in magnification of total lens system to $m_2$. The value of $\left|\frac{m_1}{m_2}\right|$ is $\_\_\_\_$ .

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 $\_\_\_\_$

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 prism of angle $75^{\circ}$ and refractive index $\sqrt{3}$ is coated with thin film of refractive index 1.5 only at the back exit surface. To have total internal reflection at the back exit surface the incident angle must be $\_\_\_\_$

$\left(\sin 15^{\circ}=0.25\right.$ and $\left.\sin 25^{\circ}=0.43\right)$

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.

Light ray incident along a vector $\overrightarrow{A O}(\overrightarrow{A O}=2 \hat{i}-3 \hat{j})$ emerges out along vector $\overrightarrow{O B}(\overrightarrow{O B}=C \hat{i}-4 \hat{j})$ as shown in the figure below. The value of $C$ is $\_\_\_\_$ .

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 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 $4 R$ in front of spherical interface. The magnitude of the magnification of point source image is $\_\_\_\_$ .

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 ?

An object $A B$ 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 ray of light passing through an equilateral prism is having velocity $2.12 \times 10^8 \mathrm{~m} / \mathrm{s}$ in the prism material, then the minimum angle of deviation is

$\_\_\_\_$ degrees.

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 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 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.

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 ________.

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

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 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 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

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 mirror is used to produce an image with magnification of $\frac{1}{4}$. If the distance between object and its image is 40 cm, then the focal length of the mirror is ________.

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?

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 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 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 :

When an object is placed 40 cm away from a spherical mirror an image of magnification $\frac{1}{2}$ is produced. To obtain an image with magnification of $\frac{1}{3}$, the object is to be moved :

Consider following statements for refraction of light through prism, when angle of deviation is minimum.

A. The refracted ray inside prism becomes parallel to the base.

B. Larger angle prisms provide smaller angle of minimum deviation.

C. Angle of incidence and angle of emergence becomes equal.

D. There are always two sets of angle of incidence for which deviation will be same except at minimum deviation setting.

E. Angle of refraction becomes double of prism angle.

Choose the correct answer from the options given below :

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

( C is the center of curvature of the spherical surface and R is the radius of curvature)

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

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

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 :

Two identical symmetric double convex lenses of focal length f are cut into two equal parts L₁, L₂ by AB plane and L₃, L₄ by XY plane as shown in figure respectively. The ratio of focal lengths of lenses L₁ and L₃ is

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

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 thin prism $\mathrm{P}_1$ with angle $4^{\circ}$ made of glass having refractive index 1.54 , is combined with another thin prism $\mathrm{P}_2$ made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism $\mathrm{P}_2$ in degrees is

A hemispherical vessel is completely filled with a liquid of refractive index $\mu$. A small coin is kept at the lowest point $(\mathrm{O})$ 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 photograph of a landscape is captured by a drone camera at a height of 18 km . The size of the camera film is $2 \mathrm{~cm} \times 2 \mathrm{~cm}$ and the area of the landscape photographed is $400 \mathrm{~km}^2$. The focal length of the lens in the drone camera is :

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

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 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 $f_2$ will be

A concave mirror of focal length $f$ in air is dipped in a liquid of refractive index $\mu$. Its focal length in the liquid will be:

The refractive index of the material of a glass prism is $\sqrt{3}$. The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism?

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 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 $P O=P I$. The distance $P O$ equals to

Given a thin convex lens (refractive index $\mu_2$ ), kept in a liquid (refractive index $\mu_1, \mu_1<\mu_2$ ) having radii of curvatures $\left|R_1\right|$ and $\left|R_2\right|$. 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 symmetric thin biconvex lens is cut into four equal parts by two planes $A B$ and $C D$ as shown in figure. If the power of original lens is 4D then the power of a part of the divided lens is

In the diagram given below, there are three lenses formed. Considering negligible thickness of each of them as compared to $\left|R_1\right|$ and $\left|R_2\right|$, i.e., the radii of curvature for upper and lower surfaces of the glass lens, the power of the combination is

Given is a thin convex lens of glass (refractive index $\mu$ ) and each side having radius of curvature $R$. One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself?

The following figure represents two biconvex lenses $L_1$ and $L_2$ having focal length $10 \mathrm{~cm}$ and $15 \mathrm{~cm}$ respectively. The distance between $L_1$ & $L_2$ is :

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 :

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

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:

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

An effective power of a combination of 5 identical convex lenses which are kept in contact along the principal axis is $25 \mathrm{D}$. Focal length of each of the convex lens is:

In an experiment to measure focal length ($f$) of convex lens, the least counts of the measuring scales for the position of object (u) and for the position of image (v) are $\Delta u$ and $\Delta v$, respectively. The error in the measurement of the focal length of the convex lens will be:

The refractive index of a prism with apex angle $A$ is $\cot A / 2$. The angle of minimum deviation is :

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

A convex mirror of radius of curvature $30 \mathrm{~cm}$ forms an image that is half the size of the object. The object distance is :

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

If the refractive index of the material of a prism is $\cot \left(\frac{A}{2}\right)$, where $A$ is the angle of prism then the angle of minimum deviation will be

Identify the physical quantity that cannot be measured using spherometer :

A convex lens of focal length $40 \mathrm{~cm}$ forms an image of an extended source of light on a photoelectric cell. A current I is produced. The lens is replaced by another convex lens having the same diameter but focal length $20 \mathrm{~cm}$. The photoelectric current now is :

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-

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

When one light ray is reflected from a plane mirror with $30^{\circ}$ angle of reflection, the angle of deviation of the ray after reflection is :

The critical angle for a denser-rarer interface is $45^{\circ}$. The speed of light in rarer medium is $3 \times 10^{8} \mathrm{~m} / \mathrm{s}$. The speed of light in the denser medium is:

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

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

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: The phase difference of two light waves change if they travel through different media having same thickness, but different indices of refraction.

Reason R: The wavelengths of waves are different in different media.

In the light of the above statements, choose the most appropriate answer from the options given below

A 2 meter long scale with least count of $0.2 \mathrm{~cm}$ is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at $80 \mathrm{~cm}$ mark and $1 \mathrm{~m}$ mark, respectively. The image of the object pin on the other side of lens coincides with image pin that is kept at $180 \mathrm{~cm}$ mark. The $\%$ error in the estimation of focal length is:

A monochromatic light wave with wavelength $\lambda_{1}$ and frequency $v_{1}$ in air enters another medium. If the angle of incidence and angle of refraction at the interface are $45^{\circ}$ and $30^{\circ}$ respectively, then the wavelength $\lambda_{2}$ and frequency $v_{2}$ of the refracted wave are:

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 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 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 scientist is observing a bacteria through a compound microscope. For better analysis and to improve its resolving power he should. (Select the best option)

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 :

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 :

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

The power of a lens (biconvex) is $1.25 \mathrm{~m}^{-1}$ in particular medium. Refractive index of the lens is 1.5 and radii of curvature are $20 \mathrm{~cm}$ and $40 \mathrm{~cm}$ respectively. The refractive index of surrounding medium:

As shown in the figure, after passing through the medium 1 . The speed of light $v_{2}$ in medium 2 will be :

$\left(\right.$ Given $\mathrm{c}=3 \times 10^{8} \mathrm{~ms}^{-1}$ )

In normal adujstment, for a refracting telescope, the distance between objective and eye piece is $30 \mathrm{~cm}$. The focal length of the objective, when the angular magnification of the telescope is 2 , will be :

A microscope was initially placed in air (refractive index 1). It is then immersed in oil (refractive index 2). For a light whose wavelength in air is $\lambda$, calculate the change of microscope's resolving power due to oil and choose the correct option.

Light travels in two media $M_{1}$ and $M_{2}$ with speeds $1.5 \times 10^{8} \mathrm{~ms}^{-1}$ and $2.0 \times 10^{8} \mathrm{~ms}^{-1}$ respectively. The critical angle between them is :

For an object placed at a distance 2.4 m from a lens, a sharp focused image is observed on a screen placed at a distance 12 cm from the lens. A glass plate of refractive index 1.5 and thickness 1 cm is introduced between lens and screen such that the glass plate plane faces parallel to the screen. By what distance should the object be shifted so that a sharp focused image is observed again on the screen?

Which of the following statement is correct?

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 $v_{\mathrm{A}}$ and $v_{\mathrm{B}}$ are velocities of light in $A$ and $B$ materials respectively.)

The speed of light in media 'A' and 'B' are $2.0 \times {10^{10}}$ cm/s and $1.5 \times {10^{10}}$ cm/s respectively. A ray of light enters from the medium B to A at an incident angle '$\theta$'. If the ray suffers total internal reflection, then

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 -

The aperture of the objective is 24.4 cm. The resolving power of this telescope, if a light of wavelength 2440 $\mathop A\limits^o $ is used to see th object will be :

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 figures). Choose the incorrect option for the reported pieces.

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 light wave travelling linearly in a medium of dielectric constant 4, incidents 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)

The difference of speed of light in the two media A and B (v_A $-$ v_B) is 2.6 $\times$ 10⁷ 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 $\times$ 10⁸ ms^$-$1)

As the beam enters the medium, it will

The speed of light in the medium is

The incident angle $\theta $ for which the light ray grazes along the wall of the rod is :