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:
Wavelength of light beam (λ) = 500 nm =500 x 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 x 10-3 m
It is related to the order of minima as:
n λ = xd/D
d = n λD/x
= 1 x 500 x10-9 x1/ 2.5 x 10-3 = 2 x 10-4 m = 0.2 mm
Therefore, the width of the slits is 0.2 mm.
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