Ray Optics · JEE Main previous year questions

A small bulb is placed at the bottom of a tank containing water to a depth of $\sqrt{7}\text{ m}$. The refractive index of water is $\frac{4}{3}$. The area of the surface of water through which light from the bulb can emerge out is $x\pi {\text{ m}}^2$. The value of x is ________.

The difference of speed of light in the two media A and B $(v_{\mathrm{A}}-v_{\mathrm{B}})$ is $2.6\times 10^7\text{ m/s}$. 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 $c=3\times 10^8{\text{ ms}}^{-1}$)

1. A.$1.303$
2. B.$1.318$
3. C.$1.13$
4. D.$0.12$

A ray of light is incident at an angle of incidence $60^{\circ }$ on the glass slab of refractive index $\sqrt{3}$. After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray is $4\sqrt{3}\mathrm{cm}$. The thickness of the glass slab is ____ $\mathrm{cm}$.

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

The difference in the number of waves when yellow light propagates through air and vacuum columns of the same thickness is one. The thickness of the air column is __________ mm. [Refractive index of air = 1.0003, wavelength of yellow light in vacuum = $6000\text{ A˚}$]

A ray of laser of a wavelength 630 nm is incident at an angle of $30^{\circ }$ at the diamond-air interface. It is going from diamond to air. The refractive index of diamond is 2.42 and that of air is 1. Choose the correct option.

1. A.angle of refraction is $24.41^{\circ }$
2. B.angle of refraction is $30^{\circ }$
3. C.refraction is not possible
4. D.angle of refraction is $53.4^{\circ }$

A prism of refractive index $\mu$ and angle of prism A is placed in the position of minimum angle of deviation. If minimum angle of deviation is also A, then the value of A in terms of refractive index is

1. A.$2{\cos }^{-1}\left(\frac{\mu }{2}\right)$
2. B.${\sin }^{-1}\left(\frac{\mu }{2}\right)$
3. C.${\sin }^{-1}\left(\sqrt{\frac{\mu -1}{2}}\right)$
4. D.${\cos }^{-1}\left(\frac{\mu }{2}\right)$

1. A.${\sin }^{-1}\frac{\sqrt{7}}{3}$
2. B.${\sin }^{-1}\frac{\sqrt{5}}{4}$
3. C.${\sin }^{-1}\frac{\sqrt{7}}{4}$
4. D.${\sin }^{-1}\frac{\sqrt{5}}{3}$

1. A.${\sin }^{-1}(\tan r)$
2. B.${\sin }^{-1}(\cot r)$
3. C.${\sin }^{-1}(\tan r^{\prime })$
4. D.${\tan }^{-1}(\sin i)$

A ray of light passing through a prism ($\mu =\sqrt{3}$) suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. Then, the angle of prism is ________ (in degrees).

An object viewed from a near point distance of 25 cm, using a microscopic lens with magnification '6', gives an unresolved image. A resolved image is observed at infinite distance with a total magnification double the earlier using an eyepiece along with the given lens and a tube of length 0.6 m, if the focal length of the eyepiece is equal to __________ cm.

1. A.green
2. B.blue and green
3. C.blue
4. D.red

The speed of electrons in a scanning electron microscope is $1\times 10^7\mathrm{m}{\mathrm{s}}^{-1}$. If the protons having the same speed are used instead of electrons, then the resolving power of scanning proton microscope will be changed by a factor of :

1. A.$\frac{1}{1837}$
2. B.1837
3. C.$\sqrt{1837}$
4. D.$\frac{1}{\sqrt{1837}}$

1. A.Statements (B) and (C) are true
2. B.Only statements (A) and (B) are true
3. C.Statements (A), (B) and (C) are true
4. D.Only statement (D) is true

A short straight object of height 100 cm lies before the central axis of a spherical mirror whose focal length has absolute value | f | = 40 cm. The image of object produced by the mirror is of height 25 cm and has the same orientation of the object. One may conclude from the information :

1. A.Image is real, same side of convex mirror.
2. B.Image is virtual, opposite side of convex mirror.
3. C.Image is virtual, opposite side of concave mirror.
4. D.Image is real, same side of concave mirror.

The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors $\vec{a},\vec{b}$ and $\vec{c}$ respectively. Then choose the correct relation for these vectors.

1. A.$\vec{b}=\vec{a}+2\vec{c}$
2. B.$\vec{b}=\vec{a}-2(\vec{a}\cdot \vec{c})\vec{c}$
3. C.$\vec{b}=2\vec{a}+\vec{c}$
4. D.$\vec{b}=\vec{a}-\vec{c}$

Given below are two statements : one is labeled as Assertion A and the other is labeled as Reason R. Assertion A : For a simple microscope, the angular size of the object equals the angular size of the image. Reason R : Magnification is achieved as the small object can be kept much closer to the eye than 25 cm and hence it subtends a large angle. In the light of the above statements, choose the most appropriate answer from the options given below :

1. A.A is true but R is false
2. B.A is false but R is true
3. C.Both A and R are true and R is the correct explanation of A
4. D.Both A and R are true but R is NOT the correct explanation of A

A point like object is placed at a distance of 1 m in front of a convex lens of focal length 0.5 m. A plane mirror is placed at a distance of 2 m behind the lens. The position and nature of the final image formed by the system is :

1. A.2.6 m from the mirror, real
2. B.1 m from the mirror, real
3. C.2.6 m from the mirror, virtual
4. D.1 m from the mirror, virtual

A double convex lens has power P and same radii of curvature R of both the surfaces. The radius of curvature of a surface of a plano-convex lens made of the same material with power 1.5 P is :

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

When an object is kept at a distance of 30 cm from a concave mirror, the image is formed at a distance of 10 cm from the mirror. If the object is moved with a speed of $9\mathrm{cm}{\mathrm{s}}^{-1}$, the speed (in $\mathrm{cm}{\mathrm{s}}^{-1}$) with which image moves at that instant is _______.

1. A.Inverted, real and unmagnified
2. B.Inverted, real and magnified
3. C.Erect, virtual and magnified
4. D.Erect, virtual and unmagnified