Optics PYQ — Page 8

The ratio of intensities at two points $P$ and $Q$ on the screen in a Young's double slit experiment where phase difference between two waves of same amplitude are $\frac{\pi }{3}$ and $\frac{\pi }{2}$, respectively are

An object is placed on the principal axis of convex lens of focal length $10\mathrm{cm}$ as shown. A plane mirror is placed on the other side of lens at a distance of $20\mathrm{cm}$. The image produced by the plane mirror is $5\mathrm{cm}$ inside the mirror. The distance of the object from the lens is ____ $\mathrm{cm}$. 

Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are $2.8$ (medium –$1$) and $6.8$ (medium – $2$), respectively. To satisfy the condition, so that the reflected and refracted rays are perpendicular to each other, the angle of incidence should be ${\mathrm{tan}}^{-1}{(1+\frac{10}{\theta })}^{\frac{1}{2}}$, the value of $\theta$ is ______. (Given for dielectric media, ${\mu }_{r}=1$)

In Young's double slits experiment, the position of 5$^{th}$ bright fringe from the central maximum is $5\mathrm{cm}$. The distance between slits and screen is $1m$ and wavelength of used monochromatic light is $600\mathrm{nm}$. The separation between the slits is:

In a Young’s double slit experiment, the intensities at two points, for the path difference $\frac{\lambda }{4}$ and $\frac{\lambda }{3}$ ($\lambda$ being the wavelength of light used) are ${I}_{1}$ and ${I}_{2}$ respectively. If ${I}_{0}$ denotes the intensity produced by each one of the individual slits, then $\frac{{I}_{1}+{I}_{2}}{{I}_{0}}=______$.

A single slit of width $a$ is illuminated by a monochromatic light of wavelength $600\mathrm{nm}$. The value of $a$ for which first minimum appears at $\theta ={30}^{o}$ on the screen will be :

A thin prism ${P}_{1}$ with an angle $6^{\circ}$ and made of glass of refractive index $1.54$ is combined with another prism ${P}_{2}$ made from glass of refractive index $1.72$ to produce dispersion without average deviation. The angle of prism ${P}_{2}$ is :

In an experiment for estimating the value of focal length of converging mirror, image of an object placed at $40\mathrm{cm}$ from the pole of the mirror is formed at distance $120\mathrm{cm}$ from the pole of the mirror. These distances are measured with a modified scale in which there are $20$ small divisions in $1\mathrm{cm}$. The value of error in measurement of focal length of the mirror is $\frac{1}{K}\mathrm{cm}$. The value of $K$ is ______.

In a reflecting telescope, a secondary mirror is used to:

A thin cylindrical rod of length $10\mathrm{cm}$ is placed horizontally on the principle axis of a concave mirror of focal length $20\mathrm{cm}$. The rod is placed in a such a way that mid point of the rod is at $40\mathrm{cm}$ from the pole of mirror. The length of the image formed by the mirror will be $\frac{x}{3}\mathrm{cm}$. The value of $x$ is ______.

‘$n$’ polarizing sheets are arranged such that each makes an angle $45^{\circ}$ with the proceeding sheet. An unpolarized light of intensity $I$ is incident into this arrangement. The output intensity is found to be $\frac{I}{64}$ . The value of $n$ will be:

In a Young’s double slit experiment, the ratio of amplitude of light coming from slits is $2:1$. The ratio of the maximum to minimum intensity in the interference pattern is

The refractive index of a transparent liquid filled in an equilateral hollow prism is $\sqrt{2}$. The angle of minimum deviation for the liquid will be _______$^{\circ}$.

As shown in the figure, a plane mirror is fixed at a height of $50\mathrm{cm}$ from the bottom of tank containing water $(\mu =\frac{4}{3})$. The height of water in the tank is $8\mathrm{cm}$. A small bulb is placed at the bottom of the water tank. The distance of image of the bulb formed by mirror from the bottom of the tank is ______ $\mathrm{cm}$. 

A vessel of depth $d$ is half filled with oil of refractive index ${n}_{1}$ and the other half is filled with water of refractive index ${n}_{2}.$ The apparent depth of this vessel when viewed from above will be-

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: The phase difference of two light waves change if they travel through different media having same thickness, but different indices of refraction. Reason R: The wavelengths of waves are different in different media. In the light of the above statements, choose the most appropriate answer from the options given below

Given below are two statements : Statement I : If the Brewster's angle for the light propagating from air to glass is ${\theta }_{B}$, then Brewster's angle for the light propagating from glass to air is $\frac{\pi }{2}-{\theta }_{B}$. Statement II : The Brewster's angle for the light propagating from glass to air is ${\mathrm{tan}}^{-1}({\mu }_{g})$, where ${\mu }_{g}$ is the refractive index of glass. In the light of the above statements, choose the correct answer from the options given below :

The critical angle for a denser-rarer interface is $45^{\circ}$. The speed of light in rarer medium is $3\times {10}^{8}m{s}^{-1}$. The speed of light in the denser medium is:

In a Young’s double slit experiment, two slits are illuminated with a light of wavelength $800\mathrm{nm}$. The line joining ${A}_{1}P$ is perpendicular to ${A}_{1}{A}_{2}$ as shown in the figure. If the first minimum is detected at $P$, the value of slits separation $a$ will be :  The distance of screen from slits $D=5\mathrm{cm}$.

Two polaroids $A\text{and}B$ are placed in such a way that the pass-axis of polaroids are perpendicular to each other. Now, another polaroid $C$ is placed between $A\text{and}B$ bisecting angle between them. If intensity of unpolarised light is ${I}_{0}$ then intensity of transmitted light after passing through polaroid $B$ will be :

A $2$ meter long scale with least count of $0.2\mathrm{cm}$ is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at $80\mathrm{cm}$ mark and $1m$ mark, respectively. The image of the object pin on the other side of lens coincides with image pin that is kept at $180\mathrm{cm}$ mark. The $%$ error in the estimation of focal length is:

Two light waves of wavelengths $800$ and $600\mathrm{nm}$ are used in Young's double slit experiment to obtain interference fringes on a screen placed $7m$ away from plane of slits. If the two slits are separated by $0.35\mathrm{mm}$, then shortest distance from the central bright maximum to the point where the bright fringes of the two wavelength coincide will be ______ $\mathrm{mm}$.

The width of fringe is $2\mathrm{mm}$ on the screen in a double slit experiment for the light of wavelength of $400\mathrm{nm}$. The width of the fringe for the light of wavelength $600\mathrm{nm}$ will be:

The radius of curvature of each surface of a convex lens having refractive index $1.8$ is $20\mathrm{cm}$. The lens is now immersed in a liquid of refractive index $1.5$. The ratio of power of lens in air to its power in the liquid will be $x:1$. The value of $x$ is