Re: Lens and light questions

[rshotwel@ivy.tec.in.us (Allen Shotwell)]

> Lens  and Light Questions
>
> (1) If I have an assemtrical diverging glass lens, i.e.  a lens with 2
> different radii of curvatures, say R1 = +10 cm and R2 = +20 cm or R1 =
> +10 cm and R2 = -20cm, I can calculate the focal length of these lenses
> using the lens makers equation. But on a ray diagram, where,
> geometrically is the focal length measured from?

Although I'm a little rusty on this one, I seem to recall that in a ray
diagram of a thin lens we ignore the thickness of the lens and assume all
the refraction takes place in the plane (using a 2d picture) that is in the
physical center of the lens and perpindicular to the optic axis. The focal
length is then measured from this plane and along the optic axis. Does this
seem right to everyone else?

> (2) At "Brewster's angle" a reflected light ray is maximally polorized
> parallel to the reflecting surface. What happens to the degree of
> polorization of the reflected light ray at angles greater than
> Brewster's angle, (of course all angles are measured from the normal
> with the incident surface.)

Using the Fresnel equations, the reflectance for the light polarized
perpindicular to the plane of incidence (Rpr) is

Rpr = sin^2(theta1-thetat)/sin^2(thetai+thetat)

and the reflectance for the light polarized parallel to the plane of
incidence (Rpl) is

Rpl = sin^2(thetai-thetat)/sin^2(thetai+thetat)

where thetai is the angle of incidence and thetat is the angle of
transmission. When thetai=thetat, Rpl is zero and the light parallel to the
plane of incidence is not reflected - Brewster's Law. Since thetat depends
on the wavelength of light and the types (indexes of refraction) of the
material the light is incident from and the material it reflects from,
Brewster's angle depends on these factors. If you go beyond Brewster's
angle, thetai no longer equals thetat and some of the parallel polarized
light will reflect. You're reflect beam will not be completely polarized in
other words.

Sorry for the long windedness, but I had to work through that to make sure
my intuition was right.



 
R. Allen Shotwell
Chair, Science and Math
Ivy Tech State College
Terre Haute, IN