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Problem 47.9 (RHK)

Using the expression for the intensity pattern for a three-slitgrating”:


We have to show (a) that a three-slitgratinghas 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