Question

A plane mirror of length $30cm$ is placed horizontally along with a vertical screen. A monochromatic point source of light is placed $20cm$ to the left of the left edge of the mirror, at a height of $2mm$ above the plane of the mirror. If the wavelength of light used is $6400\mathring{A}$ , then find the number of complete bright fringes formed.

Answer 1

Answer: 37

$y=(30cm)\tan \theta$
$=(30cm)\frac{0.2}{20}=0.3cm=3mm$
$\beta =\frac{\lambda D}{d}=\frac{6400\times 10^{-10}\times 0.5}{4\times 10^3}=0.08mm$
$n=\frac{y}{\beta }=\frac{3}{0.08}=\frac{300}{8}=\frac{75}{2}$
$=37.5$
So no. of complete fringe will be $37.$
(take a note first bright fringe will be at a distance of $\frac{\beta }{2}$ above edge)