Re: optics

[SCIAMANDA@edinboro.edu]

George asked:
> I need some help, back in the days just after slide rulers my professor in
> optics talked about using 2X2 matrix for doing ray tracing, does anyone
> have that information and where can I find it.  The reason that I ask is
> the current generation of calculators do matrics easily and I thought that
> it might be an interesting way to present optics
> regards george marrash

The "Intro to Optics" book by Pedrotti & Pedrotti which I will use next 
semester has a chapter on this.

The idea is to trace a ray by a column vector [y,A], where A is the 
angle of elevation of the ray to the horizontal, and y is the vertical 
(off axis) coordinate of the point on the ray being described.
As the ray propagates and is refracted, a 2x2 matrix operates on 
this column vector to generate the column vector of new values for 
y and A.  For example the matrix with row 1 = [1,0]  
and row 2 = [(n/n'-1)/R , n/n'] describes a refraction at a 
spherical interface: the angle A changes, the coordinate y does not. 

By combining all the matricies describing a  complicated system, a single 
matrix can be generated to represent the transformation of [y,A] 
between any two planes in a paraxial optical system.

Hope this is useful.
-Bob 

Bob Sciamanda           sciamanda@edinboro.edu
Dept of Physics         sciamanda@worldnet.att.net
Edinboro Univ of PA     http://www.edinboro.edu/~sciamanda/home.html