Re: Rainbow applet

[Leigh Palmer <palmer@SFU.CA>]

> This applet has helped answer several questions for me.  For example why the
> colors of a rainbow are in the order they are for both primary and secondary
> rainbows.  And why the interior of a rainbow is darker than the exterior.  But
> having now had time to more thoroughly investigate, I have some questions.
> Why
> does the angle of incidence effect the amount of light that is reflected and
> transmitted?  The answer to my second question I would guess may go a long way
> toward answering my first.  Why does the polarization of light effect the rate
> of  reflection or transmission? Any help out there?

A little bit humbler, I'll still venture that the mathematics is the
key to understanding the answers to those questions. You need to look
at the Fresnel equations which result from the application of the
electromagnetic boundary conditions to the problem of refraction at a
dielectric interface. While of course that result can be graphed, and
a java applet could be written to do so, I don't think that it would
constitute explanation. The beauty of Wang's applet is that it shows
very clearly the phenomenon of stationarity at what John Denker calls
the "caustic angle". The Fresnel equations, so far as I know, can
only be understood and appreciated by one who has derived them from
more fundamental physical premises.

The effect of polarization on the refraction of light can most easily
be seen by observing the effect on the part of the light which is not
refracted from the interface, but which is reflected. If you have a
laser pointer, try looking at the spot formed by a beam reflected
from some dielectric surface. Even a vinyl floor or Formica tabletop
will do; the phenomenon is ubiquitous. Rotate the pointer about its
axis and you will note a variation in the brightness of the spot. You
are seeing the effect of the different reflectances of different
polarizations of the incident beam. Rotate the pointer until the spot
is at minimum brightness. With this rotational angle held fixed, vary
the angle of incidence of the beam on the reflecting surface. You
should be able to find an angle at which the reflected spot has a
minimum brightness. With the pointer held at this angle, again rotate
it about its axis and you may be able to get the spot to disappear
entirely. When you are at this angle (called "Brewster's angle") the
transmittance of the surface is unity for light polarized in the
plane of incidence, that is parallel to the plane containing the beam
and the normal to the surface at the point of incidence. The beam
from the laser pointer is plane polarized, of course.

If you happen to have a piece of polaroid handy, go around examining
the polarization of light reflected from a variety of shiny surfaces
simply by looking through the polaroid. Sunlight reflected from water
or wet pavement is relatively depleted in the component polarized in
the plane of incidence (which is always vertical for horizontal
surfaces). Thus vertically polarized lenses will transmit relatively
less of this reflected light than unpolarized lenses.

Leigh