Question

A plane mirror of length $30\,cm$ is placed horizontally along with a vertical screen. A monochromatic point source of light is placed $20\,cm$ to the left of the left edge of the mirror, at a height of $2\,mm$ 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

$y=(30 \,cm ) \tan \theta$
$=(30 \,cm ) \frac{0.2}{20}=0.3 \, cm =3 \, mm$
$\beta=\frac{\lambda D}{d}=\frac{6400 \times 10^{-10} \times 0.5}{4 \times 10^{3}}=0.08 \,mm$
$n=\frac{y}{\beta}=\frac{3}{0.08}=\frac{300}{8}=\frac{75}{2}$
$=37.5$
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)