Embibe Experts Solutions for Chapter: Wave Optics, Exercise 1: JEE Main - 1 February 2023 Shift 2

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 ${\tan }^{-1}{\left(1+\frac{10}{\theta }\right)}^{\frac{1}{2}}$, the value of $\theta$ is ______.

(Given for dielectric media, ${\mu }_r=1$)

In Young’s double slit experiment, two slits $S_1$ and $S_2$ are $d$ distance apart and the separation from slits to screen is $D$ (as shown in figure). Now if two transparent slabs of equal thickness $0.1 \mathrm{mm}$ but refractive index $1.51$ and $1.55$ are introduced in the path of beam $\left(\mathrm{\lambda }=4000 \mathrm{\AA }\right)$ from $S_1$ and $S_2$ respectively. The central bright fringe spot will shift by ________ number of fringes.

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 $\frac{I_1+I_2}{I_0}=\_\_\_\_\_\_$.

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 :

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 $7 \mathrm{m}$ 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 displacement equations of two interfering waves are given by $y_1=10 \sin \left(\omega t+\frac{\pi }{3}\right) \mathrm{cm}$, $y_2=5\left[\sin \left(\omega t\right)+\sqrt{3} \cos \omega t\right] \mathrm{cm}$ respectively. The amplitude of the resultant wave is _____ $\mathrm{cm}$.

‘$n$’ polarizing sheets are arranged such that each makes an angle $45°$ 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:

As shown in the figure, in Young's double slit experiment, a thin plate of thickness $t=10 \mathrm{\mu m}$ and refractive index $\mu =1.2$ is inserted infront of slit $S_1$. The experiment is conducted in air ($\mu =1$) and uses a monochromatic light of wavelength $\lambda =500 \mathrm{nm}$. Due to the insertion of the plate, central maxima is shifted by a distance of $x{\beta }_0$. ${\beta }_0$ is the fringe-width before the insertion of the plate. The value of the $x$ is ______.