Question

Show that the angular width of the first diffraction fringe is half that of the central fringe.

Answer 1

Let λ and a be the wavelength and slit width of diffracting system, respectively. Let O be the position of central maximum.  Condition for the first minimum is given by

asinθ=mλ     .....(1)

Let θ be the angle of diffraction.

As diffraction angle is small

 ∴ sinθ ≈ θ

For the first diffraction minimum, let θ = θ₁ 

For the first minimum, take m =1

aθ₁=λ

`=>theta_1=lambda/a`

Now, angular width AB = θ₁

Angular width BC = θ₁

Angular width AC = 2θ₁

Width of central maximum = 2θ₁