390 Week 11: Light
- Polarization by scattering
- Polarization by absorption
- Polarization by reflection
These are a mnemonic device for the formulas and help you understand why the trans-
mission axis of polarizing sunglasses isvertical(to block reflected glare and scattered
skylight, both predominantly polarized parallel to the ground).Problem 7.Derive the expression for the critical angle leading to total internal reflection for rays
moving from adensemedium (highn) to alighterone (with lowern).Problem 8.Suppose a layer of oilno= 5/4 is floating on waternw= 4/3, that in turn is on a piece of
glassng= 3/2. Show that the critical angle for the glass is not changed by thecombined
systemof layers of water and oil; that rays incident on the glass-water interface at or
above the critical angle for glass-air alone do not escape the final layer of oil.Problem 9.Show that in spite of the occurrence of total internal reflection,one canin principlestill
see all of bottom in a shallow lake stretched out before your feet. That is, although some
rays of light from a fish on the bottom are trapped and escape, there are others that will
reach your eye no matter where your eye is located. (Other factors – ripples, reflections
off of the surface, murkiness in the water – may limit your vision, but itisn’t that any
part of the bottom istheoreticallyinvisible because light from there cannot escape to
reach your eye, it is that the light that does reach them may be veryfaint and difficult
to resolve from other things going on.)
Note that the “answer” to this question is likely to be a diagram or figure that illustrates
the answer, not algebra per se, although one can always support the answer further with
algebra.Problems 10 and 11 on next page