First slide

Diffraction

Question

If I₀ 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?

Moderate

A

$I_{0}$
B

$\frac{I_{0}}{2}$
C

$2 I_{0}$
D

$4 I_{0}$

Solution

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 N². If you double the slit width, you need 2N phasors, The intensity at the central maximum is proportional to (2N)² and is, therefore, four times the intensity for the narrow slit.

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