Re: [Phys-l] paraxial approximation

["Bob Sciamanda" <trebor@winbeam.com>]

Karl,
The no approximation ray tracing program "Snell Trace" is a quick way to 
show these effects.
Links to Snell Trace (free) are at my web site (below).

Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
trebor@winbeam.com
http://www.winbeam.com/~trebor/
----- Original Message ----- 
From: "Bob Sciamanda" <trebor@winbeam.com>
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Sent: Thursday, April 10, 2008 11:06 AM
Subject: Re: [Phys-l] paraxial approximation


> Carl,
> The typical development of the paraxial approximation involves 
> approximating
> sines and cosines by their first order expansions.  This includes not only
> the angle which a ray makes with the optical axis, but also the angle 
> which
> a ray makes with the normal to the spherical refracting/refracting 
> surface.
> This latter angle can be large for a ray parallel to the axis depending on
> where it strikes the spherical refracting/reflecting surface.
> (Refer to the development in any optics text)
>
> Bob Sciamanda