Question

A beam of light wavelength $400nm$ falls on a narrow slit and the resulting diffraction pattern is observed on a screen $2m$ away from the slit. It is observed that $2^{nd}$ order minima occurs at a distance of $2mm$ from the position of central maxima. Find the width of the slit.

Answer 1

$x=(2n+1)\frac{\lambda D}{2d}$ $n⟹2$ $D⟹2$
$x=2mm=2\times {10}^{-3}$
$\lambda =400nm$
$=400\times {10}^{-9}$
$d⟹(2\times 2+1)\times \frac{400\times {10}^{-9}\times 2}{2\times 2\times {10}^{-3}}$
$d⟹\frac{5\times 400\times {10}^{-6}}{2}$
$⟹1000\times {10}^{-6}$
$d⟹{10}^{-6}m$
$⟹1mm$