Question

In a Young's double slit experiment, $\text{I}_{0}$ is the maximum intensity and $\beta $ is the fringe width. Intensity at point $\text{P}$ which is distance $\text{x}$ from central maxima is

• A. $I_{0}cos\frac{\pi x}{\beta }$
• B. $4I_{0}cos^{2}\frac{\pi x}{\beta }$
• C. $I_{0}cos^{2}\frac{\pi x}{\beta }$
• D. $\frac{I_{0}}{4}cos^{2}\frac{\pi x}{\beta }$

Answer 1

Answer: (C)

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