(a) Explain, with suitable reasoning, why the central maximum in the single-slit Fraunhofer diffraction pattern is both wider and more intense than each secondary maximum.
(b) Starting from the intensity expression I=I0(βsinβ)2 where β=λπasinθ, obtain an expression for the angular width of the central maximum.
(c) Using the expression obtained in part (b), discuss qualitatively how the angular width of the central maximum changes when:
(i) the slit width a is doubled while the wavelength remains unchanged, and
(ii) the wavelength λ is halved while the slit width remains unchanged.