Question

What must be the ratio of the slit width to the wavelength for a single slit to have the first diffraction minimum at 45.0°?

Answer 1

Given : θ = 45°, m = 1

a sin θ = mλ for (m = 1, 2, 3... minima)

Here, m = 1 (First minimum)

a sin 45° = (1) λ

∴ a/λ = 1/sin 45° = 1.414

This is the required ratio.