Question

In a Young’s double slit experiment, $I_0$ 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. $I_{0}cos\left(\frac{\pi x}{\beta }\right)$
• B. $4I_{0}cos\left(\frac{\pi x}{\beta }\right)$
• C. $I_{0}co{s}^2\left(\frac{\pi x}{\beta }\right)$
• D. $4I_{0}co{s}^2\left(\frac{\pi x}{\beta }\right)$

Answer 1

The correct option is C

$I_{0}co{s}^2\left(\frac{\pi x}{\beta }\right)$

Path difference at Point $P=\frac{xd}{D}$

Phase difference at point $P=\frac{2\pi }{\lambda }\frac{xd}{D}=\frac{2\pi x}{\beta }$

$I_0=4I_1,$ intensity at point p

$I=I_1+I_1+2I_{1}cos\frac{2\pi x}{\beta }=2I_1[1+cos\frac{2\pi x}{\beta }]$

=$I_{0}co{s}^2\frac{\pi x}{\beta }$