Question

laser light sent through a double slit produces an interference pattern on a screen 3.0 m from the slits. If the eighth order maximum occurs at an angle of 12.0, at what angle does the third order maximum occur

Answer 1

Solution :

Given the laser light which is sent through the double slit produces an interference pattern on the screen placed 3  meters from the slits.

The 8th order maximum occurs at angle = 12

So,

$8^{th} \text{ order maxima} = d \sin \theta = m \lambda$      , m = 8

$d = \frac{8 \lambda}{\sin 12}$

$\frac{\lambda}{d}= \frac{\sin 12}{8}$

$3^{rd} \text{ order maxima}= d \sin \theta_2 = m_2 \lambda$

$\sin \theta_2 = \frac{m_2 \lambda}{d}=\frac{3 \lambda}{d}$ $=0.75\ {\sin 12}$

$\theta_2 = \sin^{-1}\left(0.75\ \sin 12\right)$

   $= \sin^{-1}\left(0.155)$

   $=8.91^\circ$