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,
[tex]$8^{th} \text{ order maxima} = d \sin \theta = m \lambda$[/tex] , m = 8
[tex]$d = \frac{8 \lambda}{\sin 12}$[/tex]
[tex]$\frac{\lambda}{d}= \frac{\sin 12}{8}$[/tex]
[tex]$3^{rd} \text{ order maxima}= d \sin \theta_2 = m_2 \lambda$[/tex]
[tex]$\sin \theta_2 = \frac{m_2 \lambda}{d}=\frac{3 \lambda}{d}$[/tex] [tex]$=0.75\ {\sin 12}$[/tex]
[tex]$\theta_2 = \sin^{-1}\left(0.75\ \sin 12\right)$[/tex]
[tex]$ = \sin^{-1}\left(0.155)$[/tex]
[tex]$=8.91^\circ$[/tex]
