Question

In a Young's double slit experiment, $I_{o}$ is the intensity at the central maximum and $\beta$ is the fringe width. The intensity at a point $P$ distant $x$ from the centre will be

• A. $I_{o} \cos \frac{\pi x}{\beta}$
• B. $4 I_{o} \cos ^{2} \frac{\pi x}{\beta}$
• C. $I_{o} \cos ^{2} \frac{\pi x}{\beta}$
• D. $\frac{I_{o}}{4} \cos ^{2} \frac{\pi x}{\beta}$

Answer 1

Answer: (C)

Path difference at point $P=\frac{x d}{D}$
Phase difference at point $P=\frac{2 \pi}{\lambda} \frac{x d}{D}=\frac{2 \pi x}{\beta}$
$I_{0}=4 I_{1}$, intensity at point $P$
$I=I_{1}+I_{1}+2 I_{1} \cos \frac{2 \pi x}{\beta}=2 I_{1}\left[1+\cos \frac{2 \pi x}{\beta}\right]$
$=I_{0} \cos ^{2} \frac{\pi x}{\beta}$