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. $I_{o}cos\left(\frac{\pi x}{\beta }\right)$
• B. $4I_{o}co{s}^2\left(\frac{\pi x}{\beta }\right)$
• C. $I_{o}co{s}^2\left(\frac{\pi x}{\beta }\right)$
• D. $\frac{I_o}{4}co{s}^2\left(\frac{\pi x}{\beta }\right)$

Answer 1

Answer: (C)

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

At a distance $x$ phase difference is $2\pi x/\beta$
$I_x=I_{0}co{s}^2\left(\frac{\varphi }{2}\right)$
$=I_{0}co{s}^2\left(\frac{2\pi x/\beta }{2}\right)(\because \varphi =2\pi x/\beta )$
$=I_{0}co{s}^2\left(\frac{\pi x}{\beta }\right)$