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A parallel beam of light of wavelength 500 nm

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 the beam of light, λ = 500 nm

Distance between the slit and the screen, D= 1 m

Distance of the first minimum from the centre of the screen,  x = 2.5 mm = 2.5 x 10-3 m

First minima, n = 1

Consider the equation, nλ = xd/D

⇒ d = nλD/x = ( 1 x 500 x 10-9 x 1) /( 2.5 x 10-3 )

= 200 x 10-6 m

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