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

 

Solution

$y=\left(30cm\right)tan\theta$

   $=\left(30cm\right)\frac{\text{0.2}}{20}=\text{0.3}cm=3mm$

    $=\frac{\lambda D}{d}$

    $=\frac{6400\times 10^{-10}\times \text{0.5}}{4\times 10^{-3}}$

    $=800\times 10^{-7}$

    $=\text{0.08}mm$

$n=\frac{y}{w}=\frac{3}{\text{0.08}}=\frac{300}{8}=\frac{75}{2}$

  $=\text{ 37.5}$

So no. of complete fringe will be 37.
(take a note first bright fringe will be at a distance of $\frac{w}{2}$ above edge)

Hence, the correct answer is 37.