Question

In Young's double slit experiment, the intensity at a point where path difference is $\frac{\lambda}{6}$ is $I .$ If $I_{0}$ denotes the maximum intensity, $\frac{I}{I_{0}}$.

• A. $\frac{1}{\sqrt{2}}$
• B. $\frac{\sqrt{3}}{2}$
• C. $\frac{1}{2}$
• D. $\frac{3}{4}$

Answer 1

Answer: (D)

Where, $\Delta x=\frac{\lambda}{6}$
$\Delta \phi=\frac{2 \pi}{\lambda} \Delta x $
$\therefore \Delta \phi=\frac{\pi}{3} $
$I=I_{0} \cos ^{2}\left(\frac{\Delta \phi}{2}\right) $
$I=I_{0} \cos ^{2}\left(\frac{\pi}{6}\right)$
or $I=I_{0} \times \frac{3}{4}$
$\therefore \frac{I}{I_{0}}=\frac{3}{4}$