# Exam #3:Friday, March 30, 2001, 8:30 am in class

-        When we went outside with the polarizers, it was cloudy and the sky was not polarized.  Still, we saw lots of polarized light in different places.  Where did that polarized light come from?

Incident light coming in at Brewster’s angle, when it reflects, is entirely polarized.  If the incident light is close to Brewster’s angle, the reflected light is partially linearly polarized.  This is all true even if the incident light is unpolarized, as was the case that day.  Thus, when we looked around, we were observing reflected light that was partially polarized.

-        I have a flashlight and I want to produce some polarized light.  Which produces polarized light of a higher intensity: (1) sticking a polarizer onto the flashlight, or (2) reflecting the light off a piece of glass, at Brewster’s angle?

Sticking a polarizer onto the flashlight cuts the intensity exactly in half.  Reflecting the light off a piece of glass sends all of the light of one polarization into the refracted beam.  The light of the other polarization is partially reflected, and partially refracted.  (Thus the refracted beam is partially polarized).  Thus, the reflected light is less than half the original intensity, and the refracted light is more than half the original intensity.  The bottom line is that while both methods produce completely linearly polarized light, the reflection method has a lower intensity than the polarizer method.

-        If you look at a fish in a pond, the apparent depth of the fish is less than the actual depth, as discussed in class and in the book.  Suppose you look at a fish inside a spherical fish tank; the curvature of the sphere changes things somewhat in a way we haven’t discussed in class (partially a lens effect, partially the depth effect).  Is the image of the fish you see real or virtual?  Since we haven’t discussed this before, you don’t have the relevant equations, but you don’t need them to answer this question.

Even in a curved fish tank, the fish still appears to be inside the tank.  Thus, what you see is a virtual image of the fish.

-        How could you estimate the radius of curvature of a spoon, from the optical properties of the spoon?

Look at the image of your hand in the concave side of the spoon.  Change the distance between the spoon and your hand until you find roughly where the image goes from being upright (very close to the spoon) to being inverted; this is the focal point of the concave side of the spoon.  The radius of curvature is twice this distance.