#### 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.

#### Solution

Wavelength of light beam, *λ* = 500 nm = 500 × 10^{−9} m`

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

For first minima, *n* = 1

Distance between the slits = *d*

Distance of the first minimum from the centre of the screen can be obtained as:

*x* = 2.5 mm = 2.5 × 10^{−3} m

It is related to the order of minima as:

`nlambda = x d/D`

`d = (nlambdaD)/x`

`= (1xx500 xx 10^(-9) xx 1)/(2.5 xx10^(-3)) = 2xx10 ^(-4) m = 0.2 mm`

Therefore, the width of the slits is 0.2 mm.

Is there an error in this question or solution?

Solution 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. Concept: Diffraction - Seeing the Single Slit Diffraction Pattern.