Geometrical Optics — JEE Main PYQs

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 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 su …

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

The wavelength of light, while it is passing through water is 540 nm. The refractive index of water is $\frac{4}{3}$. The wavelength of the same light when it is passing through a transparent medium having refractive index of $\frac{3}{2}$ is $\_\_\_\_$ nm.

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 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 $2.4\times 10^8\text{ m/s}$ and …

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.

The exit surface of a prism with refractive index $n$ is coated with a material having refractive index $\frac{\mathrm{n}}{2}$. When this prism is set for minimum angle of deviation it exactly meets the condition of critical angle. The prism angle 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 $(5{)}^{\mathrm{k}}$. The value of k 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 …

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 …

A convex lens of refractive index 1.5 and focal length $f=18\mathrm{cm}$ is immersed in water. The difference in focal lengths of the given lens when it is in water and in air is $\alpha \times \mathrm{f}$. The value of $\alpha$ is ____.
(refractive index of water …

Five persons P₁, P₂, P₃, P₄ and P₅ 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

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

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 magnificat …

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 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.

In a microscope the objective is having focal length $f_0=2\mathrm{cm}$ and eye-piece is having focal length $f_{\mathrm{e}}=4\mathrm{cm}$. The tube length is 32 cm. The magnification produced by this microscope for normal adjustment is ______.

A prism of angle 75° and refractive index 5/3 is coated with a 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 _______. (sin 15° = 0.25 and sin 25° = 0.43)

One side of an equilateral prism is painted by a transparent material of refractive index ${\mathrm{n}}_2$. The refractive index of prism is 1.6. The minimum value of ${\mathrm{n}}_2$ required for total internal reflection from painted face is $\_\_\_\_$.

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 …

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 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 …

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 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 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 …

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 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 …

Light ray incident along a vector $\overrightarrow{\mathrm{AO}}(\overrightarrow{\mathrm{AO}}=2\hat{\mathrm{i}}-3\hat{\mathrm{j}})$ emerges out along vector $\overrightarrow{\mathrm{OB}}(\overrightarrow{\mathrm{OB}}=\mathrm{C}\hat{\mathrm{i}}-4\hat{\mathrm{j}})$ as shown in th …

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.

In the diagram given below, there are three lenses formed. Considering negligible thickness of each of them as compared to $[{\mathrm{R}}_1]$ and $[{\mathrm{R}}_2]$, 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 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 $\mathrm{R}=2\mathrm{m}$. Another car approaches him from behind with a uniform speed of …

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 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 li …

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 ?

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 $\left|{\mathrm{R}}_1\right|$ and $\left|{\mathrm{R}}_2\right|$. Its second surface is silver polished. Where should an object be plac …

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 :

Two identical symmetric double convex lenses of focal length $f$ are cut into two equal parts ${\mathrm{L}}_1,{\mathrm{L}}_2$ by AB plane and ${\mathrm{L}}_3,{\mathrm{L}}_4$ by XY plane as shown in figure respectively. The ratio of focal lengths of lenses ${\mathrm{L}}_1$ and …

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 convex lens mode 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

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 $|\mathrm{u}|>f$, is

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 bet …

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 …