Question

In Young's double slit experiment intensity at a point is $(1/4)$ of the maximum intensity. Angular position of this point is (separation between slits is $d$)

• A. $\sin^{-1} \left(\lambda /d\right)$
• B. $\sin^{-1} \left(\lambda /2d\right)$
• C. $\sin^{-1} \left(\lambda /3d\right)$
• D. $\sin^{-1} \left(\lambda /4d\right)$

Answer 1

Answer: (C)

If $a$ is the amplitude of the wave then $\frac{I_{\max }}{4}=a^{2}+a^{2}+2 \,as\,\cos \phi$
or $\cos \phi=-\frac{1}{2}$
or $\phi=\frac{2 \pi}{3}$
Corresponding path difference,
$\Delta x =\frac{\phi \times \lambda}{2 \pi}=\frac{(2 \pi / 3) \times \lambda}{2 \pi}=\frac{\lambda}{3}$
So $d \sin \theta=\frac{\lambda}{3}$
or $\theta=\sin ^{-1}\left(\frac{\lambda}{3 d}\right)$