If `I_0` is the intensity of the principal maximum in the single slit diffraction pattern. Then what will be its intensity when the slit width is doubled?

Options

A. (a) `I_0`
B. (b) `I_0/2`
C. (c) `2I_0`
D. (d) `4I_0`

Answer

D

Explanation

If you divide the original slit into N strips and represents the light from each strip, when it reaches the screen, by a phasor, then at the central maximum in the diffraction pattern you add N phasors, all in the same direction and each with the same amplitude. The intensity is therefore `N^2`. If you double the slit width, you need `2N` phasors, if they are each to have the amplitude of the each phasors you used for the narrow slit. The intensity at the central maximum is proportional to `(2N)^2` and is, therefore, four times the intensity for the narrow slit.