Question

A parallel beam of light of 500 nm falls on a narrow slit and the resulting diffraction pattern is observed on a screen 1 m away. It is observed that the first minimum is at a distance of 2.5 mm from the centre of the screen. Calculate the width of the slit.

Answer 1

Given : $\lambda =500$ nm $=500\times {10}^{-9}$ m, $D=1$ m, $y_1=2.5$ mm $=2.5\times {10}^{-3}$ m

Let the width of the slit be $d$.

Distance of first minimum of diffraction pattern from the centre, $y_1=\frac{\lambda D}{d}$

$\therefore$ $2.5\times {10}^{-3}=\frac{500\times {10}^{-9}\times 1}{d}$ $⟹d=200\times {10}^{-6}$ m $=0.2$ mm