Embibe Experts Solutions for Chapter: Wave Optics, Exercise 1: Manipur Board-2018

Prove that the superposition of two waves from two coherent sources having displacements ${\mathrm{y}}_1=\mathrm{a} \mathrm{sin\omega t}$ and ${\mathrm{y}}_2=\mathrm{a} \sin \left(\mathrm{\omega t}+\mathrm{\varphi }\right)$ at a point produce the resultant intensity $\mathrm{I}=4{\mathrm{a}}^2{\cos }^2\frac{\mathrm{\varphi }}{2}$.

The refractive index of plastic is $\sqrt{3}$. Calculate the angle of refraction for a ray of light incident at polarizing angle.

Write three points of difference between interference and diffraction.

A transmitting antenna at the top of a tower has a height $32 \mathrm{m}$ and the height of the receiving antenna is $50 \mathrm{m}$. What is the maximum distance between two such antenna for satisfactory communication in line-of-sight (LOS) mode? Given the radius of earth is $6.4\times {10}^6\mathrm{m}$.

In a Young's double slit experiment, two coherent sources each of wavelength $500 \mathrm{nm}$ are placed $0.5 \mathrm{mm}$ apart and the screen is placed $1\mathrm{m}$ away.

$\left(\mathrm{a}\right)$ Find the fringe width of the interference pattern observed on the screen

In a Young's double slit experiment, two coherent sources each of wavelength $500 \mathrm{nm}$ are placed $0.5 \mathrm{mm}$ apart and the screen is placed $1\mathrm{m}$ away.

$\left(\mathrm{b}\right)$ Find the distance of the second dark fringe and the fourth bright fringe from the central fringe.