The full width at half-maximum (FWHM) of a central diffraction maximum is defined as the angle between the two points in the pattern where the intensity is one-half that at the center of the pattern.

(a) Show that the intensity drops to one-half the maximum value when sin2 a = a2/2.

(b) Verify that a -=1.39 rad (about 80o) is a solution to the transcendental equation of (a).

(c) Show that the FWHM is Δθ = 2 sin-1(0.443λ/a), where a is the slit width. Calculate the FWHM of the central maximum for slit width

(d) 1.00λ,

(e) 5.00 λ, and

(f) 10.0 λ.