Optics PYQ — Page 6

A hemispherical vessel is completely filled with a liquid of refractive index $\mu$. A small coin is kept at the lowest point $(\mathrm{O})$ of the vessel as shown in figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point E (at the level of the vessel) is 

If the distance between object and its two times magnified virtual image produced by a curved mirror is $15\mathrm{cm}$, the focal length of the mirror must be :

A parallel beam of monochromatic light of wavelength $5000\overset{o}{A}$ is incident normally on a single narrow slit of width $0.001\mathrm{mm}$. The light is focused by convex lens on screen, placed on its focal plane. The first minima will be formed for the angle of diffraction of ______ (degree).

In a double slit experiment shown in figure, when light of wavelength $400\mathrm{nm}$ is used, dark fringe is observed at $P$. If $D=0.2m$, the minimum distance between the slits ${S}_{1}$ and ${S}_{2}$ is $\alpha \mathrm{mm}$. Write the value of $10\alpha$ to the nearest integer. 

If the refractive index of the material of a prism is $\mathrm{cot}(\frac{A}{2})$, where $A$ is the angle of prism then the angle of minimum deviation will be

The thin lens formula is:

The critical angle for total internal reflection from a medium to air is 30°...

A convex lens of focal length $40\mathrm{cm}$ forms an image of an extended source of light on a photoelectric cell. A current $I$ is produced. The lens is replaced by another convex lens having the same diameter but focal length $20\mathrm{cm}$. The photoelectric current now is

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 :

In Young's double slit experiment, light from two identical sources are superimposing on a screen. The path difference between the two lights reaching at a point on the screen is $\frac{7\lambda }{4}$. The ratio of intensity of fringe at this point with respect to the maximum intensity of the fringe is:

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, chose the correct answer from the options given below:

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

The distance between object and its two times magnified real image as produced by a convex lens is $45\mathrm{cm}$. The focal length of the lens used is ________$\mathrm{cm}$.

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

The refractive index of prism is $\mu=\sqrt{3}$ and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is _______.

In Young's double slit experiment, carried out with light of wavelength $5000 \AA$, the distance between the slits is $0.3 \mathrm{~mm}$ and the screen is at $200 \mathrm{~cm}$ from the slits. The central maximum is at $x=0 \mathrm{~cm}$. The value of $x$ for third maxima is _____$\mathrm{mm}$.

Monochromatic light of wavelength $500 \mathrm{~nm}$ is used in Young's double slit experiment. An interference pattern is obtained on a screen. When one of the slits is covered with a very thin glass plate (refractive index $=1.5$ ), the central maximum is shifted to a position previously occupied by the $4^{\text {th }}$ bright fringe. The thickness of the glass-plate is ______ $\mu \mathrm{m}$.

The width of one of the two slits in a Young's double slit experiment is 4 times that of the other slit. The ratio of the maximum of the minimum intensity in the interference pattern is:

Two coherent monochromatic light beams of intensities I and $4 \mathrm{I}$ are superimposed. The difference between maximum and minimum possible intensities in the resulting beam is $x \mathrm{I}$. The value of $x$ is $_________.

Two waves of intensity ratio $1:9$ cross each other at a point. The resultant intensities at the point, when (a) Waves are incoherent is ${I}_{1}(b)$ Waves are coherent is ${I}_{2}$ and differ in phase by ${60}^{o}$. If $\frac{{I}_{1}}{{I}_{2}}=\frac{10}{x}$, then $x=$ _________.

In an experiment to measure the focal length $(f)$ of a convex lens, the magnitude of object distance$(x)$ and the image distance$(y)$ are measured with reference to the focal point of the lens. The $y-x$ plot is shown in figure. The focal length of the lens is $_____\mathrm{cm}.$ 

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

The following figure represents two biconvex lenses $L_1$ and $L_2$ having focal length $10 \mathrm{~cm}$ and $15 \mathrm{~cm}$ respectively. The distance between $L_1 \& L_2$ is : 

In a single slit experiment, a parallel beam of green light of wavelength $550 \mathrm{~nm}$ passes through a slit of width $0.20 \mathrm{~mm}$. The transmitted light is collected on a screen $100 \mathrm{~cm}$ away. The distance of first order minima from the central maximum will be $x \times 10^{-5} \mathrm{~m}$. The value of $x$ is :