JEE Main 2021 — Optics

The focal length of a convex lens is 10 cm. Its power is:

A convex lens of focal length 20 cm forms an image...

White light is passed through a double slit and interference is observed on a screen $1.5m$ away. The separation between the slits is $0.3\mathrm{mm}$. The first violet and red fringes are formed $2.0\mathrm{mm}$ and $3.5\mathrm{mm}$ away from the central white fringes. The difference in wavelengths of red and violet light is $(\text{in}\mathrm{nm}).$

A deviation of $2^{\circ}$ is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass are $0.02$ and $0.03$ respectively and refractive index for yellow light for these glasses are $1.5$ and $1.6$ respectively. The refracting angles for crown glass prism will be ________$^{\circ}$ (in degree) (Round off to the Nearest Integer)

An object is placed at the focus of concave lens having focal length $f.$ What is the magnification and distance of the image from the optical centre of the lens?

Car $B$ overtakes another car $A$ at a relative speed of $40{ms}^{-1}$. How fast will the image of car $B$ appear to move in the mirror of focal length $10\mathrm{cm}$ fitted in car $A$, when the car $B$ is $1.9m$ away from the car $A$?

Find the distance of the image from object $O,$ formed by the combination of lenses in the figure: 

An object viewed from a near point distance of $25\mathrm{cm}$, 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 $0.6m$, if the focal length of the eyepiece is equal to ____ $\mathrm{cm}.$

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).

A ray of light passes from a denser medium to a rarer medium at an angle of incidence $i.$ The reflected and refracted rays make an angle of $90^{\circ}$ with each other. The angle of reflection and refraction are respectively $r$ and ${r}^{'}.$ The critical angle is given by, 

A ray of laser of a wavelength $630\mathrm{nm}$ 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.

Three rays of light, namely red $(R)$, green $(G)$ and blue $(B)$ are incident on the face $PQ$ of a right angled prism $PQR$ as shown in figure.  The refractive indices of the material of the prism for red, green and blue wavelength are $1.27,1.42$ and $1.49$ respectively. The colour of the ray(s) emerging out of the face $PR$ is :

Your friend is having eye sight problem. She is not able to see clearly a distant uniform window mesh and it appears to her as nonuniform and distorted. The doctor diagnosed the problem as :

The refractive index of a converging lens is $1.4$. What will be the focal length of this lens if it is placed in a medium of same refractive index ? (Assume the radii of curvature of the faces of lens are ${R}_{1}$ and ${R}_{2}$ respectively)

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

The same size images are formed by a convex lens when the object is placed at $20\mathrm{cm}$ or at $10\mathrm{cm}$ from the lens. The focal length of convex lens is

A point source of light $S$, placed at a distance $60\mathrm{cm}$ infront of the centre of a plane mirror of width $50\mathrm{cm}$, hangs vertically on a wall. A man walks infront of the mirror along a line parallel to the mirror at a distance $1.2m$ from it (see in the figure). The distance between the extreme points where he can see the image of the light source in the mirror is__$\mathrm{cm}$ 

In a Young's double slit experiment, the slits are separated by $0.3\mathrm{mm}$ and the screen is $1.5m$ away from the plane of slits. Distance between fourth bright fringes on both sides of central bright fringe is $2.4\mathrm{cm}.$ The frequency of light used is $x\times {10}^{14}\mathrm{Hz}.$

Two satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutions are $1$ hour and $8$ hours respectively. The radius of the orbit of nearer satellite is $2\times {10}^{3}\mathrm{km}.$ The angular speed of the farther satellite as observed from the nearer satellite at the instant when both the satellites are closest is $\frac{\pi }{x}rad{h}^{-1}$, where $x$ is $_______.$

A source of light is placed in front of a screen. The intensity of light on the screen is $I$. Two Polaroids ${P}_{1}$ and ${P}_{2}$ are so placed in between the source of light and screen that the intensity of light on the screen is $\frac{I}{2}$. Then the ${P}_{2}$, should be rotated by an angle of (degrees) so that the intensity of light on the screen becomes $\frac{3I}{8}$.

In Young's double slit experiment, if the source of light changes from orange to blue then:

In the Young's double slit experiment, the distance between the slits varies in time as $d(t)={d}_{0}+{a}_{0}\mathrm{sin}\omega t$; where ${d}_{0},\omega$ and ${a}_{0}$ are constants. The difference between the largest fringe width and the smallest fringe width obtained over time is given as:

In a Young's double slit experiment two slits are separated by $2\mathrm{mm}$ and the screen is placed one meter away. When a light of wavelength $500\mathrm{nm}$ is used, the fringe separation will be :

If the source of light used in a Young's double slit experiment is changed from red to violet:

An unpolarized light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emerging from the analyzer is measured as $100$ Lumens. Now, if the analyzer is rotated around the horizontal axis (direction of light) by $30^{\circ}$ in clockwise direction, the intensity of emerging light will be _______Lumens.

The image of an object placed in air formed by a convex refracting surface is at a distance of $10m$ behind the surface. The image is real and is at $\frac{{2}^{rd}}{3}$ of the distance of the object from the surface. The wavelength of light inside the surface is $\frac{2}{3}$ times the wavelength in air. The radius of the curved surface is $\frac{x}{13}m$, the value of $x$ is ______ .

Two plane mirrors ${M}_{1}$ and ${M}_{2}$ are at right angle to each other shown. A point source $P$ is placed at $a$ and $2a$ meter away from ${M}_{1}$ and ${M}_{2}$ respectively. The shortest distance between the images thus formed is : (Take $\sqrt{5}=2.3$) 

Region $I$ and $\mathrm{II}$ are separated by a spherical surface of radius $25\mathrm{cm}$. An object is kept in region $I$ at a distance of $40\mathrm{cm}$ from the surface. The distance of the image from the surface is: 

In a Young's double slit experiment, the width of the one of the slit is three times the other slit. The amplitude of the light coming from a slit is proportional to the slit-width. Find the ratio of the maximum to the minimum intensity in the interference pattern.

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 _____ $\mathrm{mm}$. [Refractive index of air $=1.0003$, the wavelength of yellow light in vacuum $=6000\overset{\circ }{A}]$

A fringe width of $6\mathrm{mm}$ was produced for two slits separated by $1\mathrm{mm}$ apart. The screen is placed $10m$ away. The wavelength of light used is $x$ $\mathrm{nm}$. The value of $x$ to the nearest integer is ______.

The thickness at the centre of a plano convex lens is $3\mathrm{mm}$ and the diameter is $6\mathrm{cm}.$ If the speed of light in the material of the lens is $2\times {10}^{8}{ms}^{-1}.$ The focal length of the lens is ___________.

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 in terms of refractive,

An object is placed beyond the centre of curvature $C$ of the given concave mirror. If the distance of the object is ${d}_{1}$ from $C$ and the distance of the image formed is ${d}_{2}$ from $C,$ the radius of curvature of this mirror is:

The expected graphical representation of the variation of angle of deviation ' $\delta$ ' with angle of incidence 'i' in a prism is :

Curved surfaces of a plano-convex lens of refractive index ${\mu }_{1}$ and a plano-concave lens of refractive index ${\mu }_{2}$ have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the combined lenses 

A ray of light entering from air into a denser medium of refractive index $\frac{4}{3}$, as shown in figure. The light ray suffers total internal reflection at the adjacent surface as shown. The maximum value of angle $\theta$ should be equal to: 

Two coherent light sources having intensity in the ratio $2x$ produce an interference pattern. The ratio $\frac{{I}_{\mathrm{max}}-{I}_{\mathrm{min}}}{{I}_{\mathrm{max}}+{I}_{\mathrm{min}}}$ will be

An object is placed at a distance of $12\mathrm{cm}$ from a convex lens. A convex mirror of focal length $15\mathrm{cm}$ is placed on another side of the lens at $8\mathrm{cm}$ as shown in the figure. The image of the object coincides with the object.  When the convex mirror is removed, a real and inverted image is formed at a position. The distance of the image from the object will be $___\mathrm{cm}$

The angle of deviation through a prism is minimum when  (A) Incident ray and emergent ray are symmetric to the prism (B) The refracted ray inside the prism becomes parallel to its base (C) Angle of incidence is equal to that of the angle of emergence (D) When angle of emergence is double the angle of incidence Choose the correct answer from the options given below :

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 $25\mathrm{cm}$ and hence it subtends a large angle. In the light of the above statements, choose the most appropriate answer from the options given below:

The light waves from two coherent sources have same intensity ${I}_{1}={I}_{2}={I}_{0}.$ In interference pattern the intensity of light at minima is zero. What will be the intensity of light at maxima?

In Young's double slit arrangement, slits are separated by a gap of $0.5\mathrm{mm}$, and the screen is placed at a distance of $0.5m$ from them. The distance between the first and the third bright fringe formed when the slits are illuminated by a monochromatic light of $5890\overset{o}{A}$ is :-

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

A prism of refractive index ${n}_{1}$ and another prism of refractive index ${n}_{2}$ are stuck together (as shown in the figure). ${n}_{1}$ and ${n}_{2}$ depend on $\lambda ,$ the wavelength of light, according to the relation ${n}_{1}=1.2+\frac{10.8\times {10}^{-14}}{{\lambda }^{2}}$ and ${n}_{2}=1.45+\frac{1.8\times {10}^{-14}}{{\lambda }^{2}}$ The wavelength for which rays incident at any angle on the interface $BC$ pass through without bending at that interface will be ____ $\mathrm{nm}.$ 

Cross-section view of a prism is the equilateral triangle $ABC$ shown in the figure. The minimum deviation is observed using this prism when the angle of incidence is equal to the prism angle. The time taken by light to travel from $P$ (midpoint of $BC$) to $A$ is ___________ $\times {10}^{-10}s.$ (Given, speed of light in vacuum $=3\times {10}^{8}m{s}^{-1}$ and $\mathrm{cos}30^{\circ}=\frac{\sqrt{3}}{2}$) 

The focal length $f$ is related to the radius of curvature $r$ of the spherical convex mirror by:

Consider the diffraction pattern obtained from the sunlight incident on a pinhole of diameter $0.1\mu m.$ If the diameter of the pinhole is slightly increased, it will affect the diffraction pattern such that