Question

A parallel beam of light of wavelength 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. Find the width of the slit.

Answer 1

Wavelength of light beam, $\lambda$

Distance of the screen from the slit, $D=1m$

For first minima, $n=1$

Distance between the slits is $d$

Distance of the first minimum from the centre of the screen can be obtained as, $x=2.5mm=2.5\times {10}^{-3}$

Now, $n\lambda =xd/D$

$\Rightarrow d=n\lambda D/x=0.2mm$

Therefore, the width of the slits is 0.2 mm.