Light
of wavelength 600 nm is
incident normally on a diffraction grating.
Two adjacent principal maxima occur at
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Solution: Click For PDF Version The grating equation is
From the
statement of the problem we have two possibilities, either the
adjacent principal maxima correspond to
As the
adjacent principal maxima occur at
and
are
consistent. The wavelength of the monochromatic light is
The size of the slit width will be determined by using the information that the 4th order principal maxima is missing. The fourth order principal maximum falls at the position a diffraction minimum produced by the finite width size of slits in the grating. The intensity diffraction envelope is determined by
The value of
If this angle is to coincide with first diffraction minimum due to the finite width of the slits, we have the condition
The second diffraction minimum will occur at
The order of the grating principal maxima that will coincide with the second diffraction minimum will be given by the condition
We note that
for
Therefore, all orders of the principal maxima that will be seen on the screen will be
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.
The fourth order is missing.
(a) We have to find the separation between
adjacent slits; (b) the
smallest possible individual slit width; and name all orders actually
occurring on the screen with the values derived in
(a) and (b).
,
or
.
,
they correspond to
,
.
Therefore, the slit separation is
.
for the 4th order
principal maximum is
.
.
Therefore, principal maxima of order
and greater will not be seen on the screen.