The figure, drawn here, shows the geometry of path differences for diffraction by a single slit of width a.

Given appropriate reasoning to explain why the intensity of light is
(i) maximum of the central point C on the screen.
(ii) (nearly) zero for point P on the screen when `theta=lamda//a`.
Hence, write an expression for the total linear width of the central maxima on a screen kept at a distance D from the plane of the slit.

Explanation

At center of screen C all wavelets :
(i) From slit meet in the same phase so they add constructively to produce a central maxima i.e., bright firnge.
(ii) When `theta=lamda//a`, path difference from two halves of slit will be `lamda//2` i.e., wavelets from two halves reach at point P in opposite phase, giving a dark or minima.
(iii) `beta_(0)=(2Dlamda)/(a)`.