Show that the angular width of the first diffraction fringe is half that of the central fringe.
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
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
Now, angular width AB = θ1
Angular width BC = θ1
Angular width AC = 2θ1
Width of central maximum = 2θ1