COMMENTS ON PROBLEM SET 10 - FALL 2002

	For the most part, all of the four problems are similar to
examples in the text, and so you can take this as a reminder that it's
your obligation to read the text.  Take that.

	One thing I would like to point out in the reading is Equation
(8.80) on Page 572, giving the different expressions for beta.  I
think the last one should be an equality, not an approximation;  see
Figure 8.24 on the previous page.  What often happens is that tan(psi)
is approximated by sin(psi), and very often "R" is taken to be the
distance from the slit to the screen, in which case x/R is indeed
tan(psi), whereas sin(psi) is needed in the derivation for
interference, and it helps to use that angle in deriving the analogous
form for diffraction.  Both of these considerations are illustrated in
the two examples on Pages 575-574.

	There are many, many approximations being used in different
uses of diffraction and interference, and knowing which are being used
goes a long way to understanding these phenomena.

	Anyway ...

	Problem 1: This problem is both qualitative and quantitative.
What is the astronomer looking for in the pattern?  How will the
pattern say anything about the smoothness of the lens blank?  In this
and similar problems, recall that the arrows represent directions of
plane waves only, and the fact that the two reflected waves have their
directions of propagation displaced does not affect the nature of the
interference pattern.

	Problem 2:  These are tranverse waves, so polarization is not
an issue, and calling the desired angle "theta" has nothing to do with
any angle from a polarization axis.  You will of course want the far
field pattern in any event.  F'heaven's sake, use a plotting program
to do the plot, and maybe even find the FWHM (Full Width Half-Maximum)
numerically for part (b).
	The question asks for an "approximate result in
degrees" for part (b), so if your plotting or numerical program uses
radians, I guess you should do the conversion.  It turns out that in
the limit of large N, the FWHM (in terms of delta, not theta as
requested in the problem) is not quite half the width
(zero-to-zero) of the main lobe, being greater by a factor of
1.12880457 (I'd be happy to explain where that comes from on
request).  This is, again, the large-N limit;  for N=2 the ratio is a
mere 1, and for N=17 the ratio is 1.27117798.
	Looking for a similar example from the text might help
in part (c).

	Problem 3:  For this one, however, there is no corresponding
example in the text, and the single source off-axis was not considered
in lecture.  You could either make a reasonable guess or rederive the
diffraction formula for an off-axis source.

	Problem 4:  You can tell by inspection that the interference
maxima are evenly spaced, indicating that sin(psi) is taken to be
equal to tan(psi);  when you find d and lambda, check that this is
indeed consistent.  For part (d), even the least sophisticated
graphing program will give you something better than you or I could do
by hand.