Optics PYQ — Page 12

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.

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

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 $\sqrt{5}=2.3$) 

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:

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

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,

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)

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

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

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 ______ .

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).

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

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 $\mathrm{cos}30^{\circ}=\frac{\sqrt{3}}{2}$) 

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 :

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

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.

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 $x\times {10}^{14}\mathrm{Hz}.$

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?

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 $_______.$

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 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.