Question

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

• A. 0.1 mm
• B. 25 mm
• C. 0.4 mm
• D. 0.5 mm

Answer 1

The correct option is D 0.5 mm

$I=I_{0}co{s}^2\frac{\left(\pi dsin\theta \right)}{\lambda }=\frac{I_0}{2}$
$cos\left(\frac{\pi dsin\theta }{\lambda }\right)=\frac{1}{\sqrt{2}}$
we get,
$x=\frac{\lambda D}{4d}=\frac{650\times {10}^{-9}\times 0.75}{4\times 0.25\times {10}^{-3}}=487.5\times {10}^{-6}m$
$=0.4875mm=0.5mm$