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Q.

A beam of light of wavelength 400 nm falls on a narrow slit and the resulting diffraction pattern is observed on a screen 2m away from the slit. It is observed that 2nd order minima occurs at a distance of 2 mm from the position of central maxima. Find the width of the slit (in mm).

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Detailed Solution

Given, 

     λ = 400 nm D = 2m y = 2mm

Question Image

 

Now, point Q is the point of second order minima.

sinθ = tanθ ≈ θ = 2×10-32 = 10-3

Let the slit separation be a.

Now for second order minima, θ = 2λa

Equating 2λa by θ = 10-3 , we obtain a = 0.8 mm

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