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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.

Solution:

Given : λ=500nm=500×10⁻⁹m, D=1m, y₁=2.5mm=2.5×10⁻³m
Let the width of the slit be d.
Distance of first minimum of diffraction pattern from the centre, y₁=λD/d
∴ 2.5×10⁻³ = 500×10⁻⁹×1/d
⇒d = 200×10⁻⁶ m = 0.2mm