Using the expression for the intensity pattern for a three-slit “grating”:
We have to show (a) that a three-slit “grating” has only one secondary maximum; (b) we have to find its location and (c) its relative intensity.
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We will first locate the extremum of the function
We will calculate and find the solutions of the equation
Therefore, the zeros of will be at
We note that the first principal maximum occurs at . We will therefore examine the nature of extremum of at
Condition of a local maximum of is that
We find that
We note that
Therefore, the secondary maximum will occur at .
The location of the secondary maximum will, therefore, be at
The relative intensity of the secondary maximum will be
We note that as the principal maxima occur at the ‘grating” condition
The first principal maximum will occur at
and the secondary maximum at