Ray Optics · JEE Main previous year questions

1. A.$1:2$
2. B.$1:1$
3. C.$2:1$
4. D.$1:4$

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

1. A.1.5
2. B.16/3
3. C.3
4. D.4

1. A.$\frac{3}{2}$
2. B.$\frac{\sqrt{3}}{2}$
3. C.$\sqrt{3}$
4. D.$\sqrt{2}$

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]

1. A.0.04
2. B.0.1
3. C.0.40
4. D.0.01

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

1. A.0.15 m
2. B.0.10 m
3. C.0.25 m
4. D.0.20 m

A plano-convex lens having radius of curvature of first surface $2\mathrm{cm}$ exhibits focal length of $f_1$ in air. Another plano-convex lens with first surface radius of curvature $3\mathrm{cm}$ 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

1. A.$2:3$
2. B.$1:3$
3. C.$1:2$
4. D.$3:5$

A photograph of a landscape is captured by a drone camera at a height of 18 km . The size of the camera film is $2\text{ cm}\times 2\text{ cm}$ and the area of the landscape photographed is $400{\text{ km}}^2$. The focal length of the lens in the drone camera is :

1. A.2.8 cm
2. B.0.9 cm
3. C.2.5 cm
4. D.1.8 cm

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:

1. A.$\mu f$
2. B.$f$
3. C.$\frac{f}{\mu }$
4. D.$\frac{f}{(\mu -1)}$

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?

1. A.$60^{\circ }$
2. B.$50^{\circ }$
3. C.$58^{\circ }$
4. D.$48^{\circ }$

1. A.$-\frac{1}{6}\left(\frac{1}{|R_1|}-\frac{1}{|R_2|}\right)$
2. B.$-\frac{1}{6}\left(\frac{1}{|R_1|}+\frac{1}{|R_2|}\right)$
3. C.$\frac{1}{6}\left(\frac{1}{|R_1|}+\frac{1}{|R_2|}\right)$
4. D.$\frac{1}{6}\left(\frac{1}{|R_1|}-\frac{1}{|R_2|}\right)$

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?

1. A.$R/\mu$
2. B.$R/(2\mu -1)$
3. C.$R/(2\mu -3)$
4. D.$\mu R$

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 $R=2\text{ m}$. Another car approaches him from behind with a uniform speed of $90\text{ km/hr}$. When the car is at a distance of $24\text{ m}$ 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 _________ ${\text{m/s}}^2$.

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 :

1. A.Statement I is false but Statement II is true
2. B.Both Statement I and Statement II are false
3. C.Both Statement I and Statement II are true
4. D.Statement I is true but Statement II is false

1. A.$25\mathrm{cm}$
2. B.$35\mathrm{cm}$
3. C.$10\mathrm{cm}$
4. D.$15\mathrm{cm}$

Average force exerted on a non-reflecting surface at normal incidence is $2.4\times 10^{-4}\text{ N}$. If $360{\text{ W/cm}}^2$ is the light energy flux during span of 1 hour 30 minutes, then the area of the surface is:

1. A.$20{\text{ m}}^2$
2. B.$0.2{\text{ m}}^2$
3. C.$0.1{\text{ m}}^2$
4. D.$0.02{\text{ m}}^2$

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:

1. A.$1:2$
2. B.$1:\sqrt{2}$
3. C.$2:1$
4. D.$\sqrt{2}:1$

1. A.$15\mathrm{cm}$ (right of second lens)
2. B.$30\mathrm{cm}$ (right of third lens)
3. C.$30\mathrm{cm}$ (left of third lens)
4. D.$15\mathrm{cm}$ (left of second lens)

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

1. A.1.2
2. B.1.5
3. C.1.4
4. D.1.8

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, choose the correct answer from the options given below :

1. A.Both Statement I and Statement II are true
2. B.Statement I is true but Statement II is false
3. C.Statement I is false but Statement II is true
4. D.Both Statement I and Statement II are false

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:

1. A.$50\mathrm{cm}$
2. B.$20\mathrm{cm}$
3. C.$25\mathrm{cm}$
4. D.$500\mathrm{cm}$

A light ray is incident on a glass slab of thickness $4\sqrt{3}\text{ cm}$ 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 ________ $\text{cm}$. (Given $\sin 15^{\circ }=0.25$)

The distance between object and its 3 times magnified virtual image as produced by a convex lens is $20\mathrm{cm}$. The focal length of the lens used is ____ $\mathrm{cm}$.

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

1. A.${\delta }_m=180^{\circ }-3\mathrm{A}$
2. B.${\delta }_m=180^{\circ }-4A$
3. C.${\delta }_m=180^{\circ }-2A$
4. D.${\delta }_m=180^{\circ }-A$

Light from a point source in air falls on a convex curved surface of radius $20\mathrm{cm}$ and refractive index 1.5. If the source is located at $100\mathrm{cm}$ from the convex surface, the image will be formed at ____ $\mathrm{cm}$ from the object.

The diffraction pattern of a light of wavelength $400\text{ nm}$ diffracting from a slit of width $0.2\text{ mm}$ is focused on the focal plane of a convex lens of focal length $100\text{ cm}$. The width of the $1^{\text{st}}$ secondary maxima will be :

1. A.$2\text{ mm}$
2. B.$0.2\text{ mm}$
3. C.$0.02\text{ mm}$
4. D.$2\text{ cm}$