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\course \hfill Russell Brown \\
Project 3  \hfill \today

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For the third project, your assignment is to complete parts 1 to 4 of
the rainbow project on page 282 and 283 of Stewart.




You are to work in groups of 2 to 5, again. Projects completed by only
one person will not be graded.
 If you wish to work with
someone in a different section, please see Brown to make arrangements.
Each group should hand in a 2-7 page report describing what you have
done and answering each of the questions from Stewart.
Please write ``Each group member contributed to the solution of this
project.'' on a cover sheet and have each group member sign indicating
that he or she agrees with this statement.


Consider the following points as you work on the project.

\begin{enumerate}
\item
Your answers to  parts 1 and 3 should be illustrated by sketches to
explain the variables involved (use the sketches in Stewart if you
wish). 

\item Please compute the angles of deviation to one more decimal place
than are given in Stewart. This will help me check that you did the
calculation and are not just repeating numbers from the text.  Be
careful about rounding intermediate answers!

\item In part 1, please try to explain why the rainbow occurs at
$\alpha$ for which $D(\alpha) $ is a minimum. (Hint: Consider the
linear approximation for $D$ near the minimum.)

\item To compute $d D/ d\alpha$, use Snell's law and implicit
differentiation to express $d\beta/d\alpha$ in terms of $\alpha$.

\item For part 2, you will probably want to find the minimum in terms
of $k$ and then evaluate at different values of $k$ to find the
angle of deviation for different colors.   I expect you will use a
similar strategy in part 4.




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