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26.45. Set Up:
Maxima are located by
where
is the angle of incidence and
d
is the separation of
crystal planes.
Solve: (a)
First maximum, so
(b)
For
For
the equation has no
solution.
Reflect:
Since
is not small, we find that
for
and there are only two
angles for which constructive interference occurs.
26.46. Set Up:
The maxima are given by
Solve: (a)
and
This is an x ray.
(b)
The equation
doesn’t have any solutions for
26.47. Set Up:
Rayleigh’s criterion says
where
s
is the distance of the
object from the lens and
Solve:
Reflect:
The focal length of the lens doesn’t enter into the calculation. In practice, it is difficult to achieve resolution
that is at the diffraction limit.
26.48. Set Up:
The diffraction is by a single slit of width
a
, not by a circular aperture. The diffraction minima are
located by
and Rayleigh’s criterion is
where
s
is the distance of the object from the
lens and
Solve:
26.49. Set Up:
Rayleigh’s criterion for circular apertures says
Solve: (a)
(b)
(c)
(d)
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 Spring '07
 Shoberg

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