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°?

Answer 1

Given: θ = 45°

m = 1

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

Here, m = 1 (first minimum)

∴ a sin 45° = (1) λ

`a/λ = 1/(sin 45°)`

`a/λ = 1/(1/sqrt2)`

= `sqrt2`

= 1.414

∴ The ratio of the slit width to the wavelength is `sqrt2` (approximately 1.414)