Optics Homework 7: Due Thurs 1/31/08
Dr. Colton, Winter 2008
20 total points
1. Undoubtedly the most important interface in optics is when air meets glass. Let’s take n = 1
for air and n = 1.54 for glass. Use Mathematica or similar program to make the following
plots for this interface, as a function of the incident angle:
(a) r and t for p-polarized light (plot together on same graph)
(b) R and T for p-polarized light (plot together on same graph)
(c) r and t for s-polarized light (plot together on same graph)
(d) R and T for s-polarized light (plot together on same graph)
Explicitly label Brewster’s angle on all of the applicable graphs.
Hint: The graphs for (a) and (b) can be found in Griffiths chapter 9 for nglass = 1.50 rather
than 1.54, so you can go there to find out if your own graphs look correct. And here are my
own graphs for (c) and (d) (also done for nglass = 1.50).
1
0.75
0.8
0.5
0.25
0.6
0.25
0.5
0.75
1
1.25
1.5
0.4
-0.25
-0.5
0.2
-0.75
-1
0.25
0.5
0.75
1
1.25
1.5
2. (8 pts) P&W, L3.7. Take care in your experimental measurements. You just did the graphs
for problem 1, so (hopefully) it shouldn’t be too hard to add experimental data points to the
graph. If you can’t figure out how to plot the points and curves together (like in P&W Fig
3.4), at least draw in the experimental points by hand on the graphs.
For possible “extra mile points”, you could try to figure out how to fit your actual
experimental data points to a theoretical curve with an unknown n2, and hence deduce
whether 1.54 is really the best guess for the glass’s index of refraction.
3. P&W, P3.12
4. Read the last paragraph of P&W section 3.7. (It begins “Brewster’s angle exists…”) Suppose
you’ve got a material that has a complex index of refraction given by n = 0.2 ad  = 3.4 (FYI:
that’s what’s listed for silver in P3.13; I’m not sure what frequency those values are valid
for). Use Mathematica or similar program to make a plot of the magnitude and phase of rp vs.
angle of incidence, and have the program determine where |rp| is a minimum, to at least 4 sig
figs.