Ray Optics — JEE Main PYQs

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 ________.

[Figure: An equilateral (triangular) prism with a ray incident on its left face; the bottom face is hatched and labelled paint ($n_2$).]

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 ________.

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.

[Figure: A rod lying along the principal axis of a concave mirror, with the near end of the rod at a distance of 20 cm from the mirror]

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 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 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 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 $AB$ is placed $15 \text{ cm}$ on the left of a convex lens $P$ of focal length $10 \text{ cm}$. Another convex lens $Q$ is now placed $15 \text{ cm}$ right of lens $P$. If the focal length of lens $Q$ is $15 \text{ cm}$, the final image 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 $4R$ in front of spherical interface. The magnitude of the magnification of point source image is ________.

[Figure: A point source $p$ on the axis at distance $4R$ to the left of a convex spherical interface of radius $R$; medium on the left has $n_1 = 1$ and medium on the right has $n_2 = 1.4$]

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 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.

A thin biconvex lens is prepared from the glass ($\mu = 1.5$) both curved surfaces of which have equal radii of $20\,\text{cm}$ 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 $\vec{AO}$ $\left(\vec{AO} = 2\hat{i} - 3\hat{j}\right)$ emerges out along vector $\vec{OB}$ $\left(\vec{OB} = C\hat{i} - 4\hat{j}\right)$ as shown in the figure below. The value of $C$ is ________.

[Figure: a ray $A$ incident at point $O$ on a horizontal interface between medium $\mu_1 = 1$ (above) and $\mu_2 = 1.5$ (below), making angle $\alpha$ with the normal above and refracting at angle $\beta$ towards $B$ below]

A slanted object AB 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 :

[Figure: a convex lens of focal length f = 20 cm; object AB slanted at angle $\alpha$ to the principal axis with A on the axis at 30 cm from the lens; B is 1 cm ahead of and 2 cm above A]

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)

[Figure: object O in medium 1 ($n_1=1$) at 0.2 m to the left of a convex spherical surface; medium 2 ($n_2=1.5$) on the right with center of curvature C at R = 0.4 m]

Two identical objects are placed in front of convex mirror and 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 convex mirror and by concave mirror is :

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 ($R_1 \neq R_2$), without any change in lens power then possible combination of $R_1$ and $R_2$ is :

A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to $60°$. The refractive index of the prism material is $\sqrt{2}$. The angle of incidence (in degrees) is _________.

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:

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 monochromatic light of frequency $5 \times 10^{14}$ Hz travelling through air, is incident on a medium of refractive index '2'. Wavelength of the refracted light will be :

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.

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 :

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 container contains a liquid with refractive index of 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 immissible)

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 __________.

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 transparent block A having refractive index $\mu = 1.25$ is surrounded by another medium of refractive index $\mu = 1.0$ as shown in figure. A light ray is incident on the flat face of the block with incident angle $\theta$ as shown in figure. What is the maximum value of $\theta$ for which light suffers total internal reflection at the top surface of the block ?

[Figure: a ray enters the vertical left face of rectangular block A ($\mu_2 = 1.25$, surrounded by $\mu_1 = 1.0$) at angle $\theta$ to the horizontal normal, refracts, and strikes the top surface at the critical angle $\theta_C$]

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 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 _______.

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 ?

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

[Figure: a container holding three layers — water ($\mu = \frac{4}{3}$) on top, a thin curved glass lens ($\mu = \frac{3}{2}$) in the middle, and water ($\mu = \frac{4}{3}$) below; the upper and lower curved surfaces of the glass lens have radii of curvature $|R_1|$ and $|R_2|$]

The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which is a convex mirror with radius of curvature $R = 2$ m. Another car approaches him from behind with a uniform speed of 90 km/hr. When the car is at a distance of 24 m from him, the magnitude of the acceleration of the image of the car in the side view mirror is 'a'. The value of 100a is ________ $\mathrm{m/s^2}$.

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 $|R_1|$ 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?

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 PO = PI. The distance PO equals to

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 ?

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 :

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 face of the lens is silvered 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

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

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 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 :

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 _____.

[Figure: a hemispherical vessel filled with liquid, rim points A and B at the top with centre C; coin at the lowest point O; point E lies outside the vessel at the level of the rim, to the right of B]

A thin prism $P_1$ with angle 4° 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

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 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 :

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 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 $\sin 15° = 0.25$)

Given below are two statements :

Statement I : When the white light passed through a prism, the red light bends lesser than yellow and violet.

Statement II : The refractive indices are different for different wavelengths in dispersive medium.

In the light of the above statements, chose the correct answer from the options given below :

The refractive index of prism is $\mu = \sqrt{3}$ and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is _________ $^\circ$.

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 :

Critical angle of incidence for a pair of optical media is 45°. The refractive indices of first and second media are in the ratio:

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

[Figure: an object 30 cm to the left of a converging lens $f_1 = 10\ \mathrm{cm}$; a diverging lens $f_2 = -10\ \mathrm{cm}$ is 5 cm to its right; a converging lens $f_3 = 30\ \mathrm{cm}$ is 10 cm further right]

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

[Figure: parallel rays enter biconvex lens $L_1$, converge and then pass through biconvex lens $L_2$, emerging parallel to the axis]

The distance between object and its 3 times magnified virtual image as produced by a convex lens is 20 cm. The focal length of the lens used is ________ cm.

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 :

Two immiscible liquids of refractive indices $\frac{8}{5}$ and $\frac{3}{2}$ 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 $\frac{\alpha}{4}$ cm. The value of $\alpha$ is ________.

[Figure: a beaker with two liquid layers, each 6 cm high — upper layer $\mu_2 = 3/2$, lower layer $\mu_1 = 8/5$ — with a coin at the bottom]

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

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.

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

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.