Question

Two slits spaced $0.25mm$ apart are placed $0.75m$ from a screen and illuminated by coherent light with a wavelength of $650nm$. The intensity at the center of the central maximum ($\theta =0^o$) is $I_0$. The distance on the screen from the center of the central maximum to the point where the intensity has fallen to $I_0/2$ is nearly

• A. $0.1mm$
• B. $0.25mm$
• C. $0.4mm$
• D. $0.5mm$

Answer 1

The correct option is D $0.5mm$

Let $x$ be the minimum distance from the central maximum then,

$\frac{I_o}{2}=I_o{\cos }^2\left(\frac{\pi x}{\beta }\right)$

$\frac{\pi x}{\beta }=\frac{\pi }{4}\Rightarrow x=\frac{\lambda D}{4d}=\frac{6.5\times {10}^{-7}\times 0.75}{4\times 0.25\times {10}^{-3}}=4.875\times {10}^{-4}m\approx 0.5mm$