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673.


Problem 47.8 (RHK)


Using the expression for the intensity pattern for a three-slit “grating”:

where

We have to show that the half-width of the fringes for a three-slit diffraction pattern, assuming small enough so that , is

.


Solution:           Click For PDF Version

 We have to find the angle near to the centre of the principal maximum where intensity is half of its maximum value, which is . That is

.

We thus have the equation

The physical solution is

Therefore,

Therefore, the half-width of the fringes for a three-slit diffraction pattern will be