(a)We
have to show that the values of
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Solution: Click For PDF Version (a)As
the condition
for maxima of the function
We have
(b) Solutions of the equation
are:
If we expect maxima to occur at midpoints of successive minima, then the locations of secondary maxima will be determined by the relation
we are
leaving out the central maxima, which corresponds to
The
deviations from the midpoint approximation can be seen from first
two values of
From the above calculations, we note that the secondary maxima lie do not lie at the midpoints of successive minima, but only closely to the midpoints.
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at which intensity maxima for single-slit diffraction occur can be
found exactly by differentiating
and the straight line
and finding their intersection. (c) We
have to find the (nonintegral)
values of m corresponding to successive
maxima in the single-slit pattern. We
may note that the secondary maxima do not lie exactly halfway
between minima.
,
is
and
.