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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Solution: Click For PDF Version (a)We will first locate the extremum of the function
We will
calculate
Therefore,
the zeros of
We note that
the first principal maximum occurs at
Condition of
a local maximum of
We find that
We note that
Therefore,
the secondary maximum will occur at
(b) The location of the secondary maximum will, therefore, be at
(c) 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
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and find the solutions of the equation
.
We will therefore examine the nature of extremum of
at
.
