Software for geometrical optics

The industrial tool is zemax; however, it is very expensive.

If you just want to make diagrams, the TeX package pst-optics might do the trick.

In the gaussian beam regime, optocad (free) is a tool often used in the laser interferometer gravitational wave detector community.

I just discovered:

opticalraytracer

From the manual:

OpticalRayTracer is a free (GPL) cross-platform application that analyzes systems of lenses and mirrors. It uses optical principles and a virtual optical bench to predict the behavior of many kinds of ordinary and exotic lens types as well as flat and curved mirrors. OpticalRayTracer includes an advanced, easy-to-use interface that allows the user to rearrange the optical configuration by dragging objects around using the mouse.

OpticalRayTracer fully analyzes lens optical properties, incuding refraction and dispersion. The dispersion display uses color-coded light beams to simplify interpretation of the results.

Recent OpticalRayTracer versions allow the creation of mirrors, flat and curved. In modern optical designs, mirrors often produce better results than lenses, for example in astronomical instruments. Such instruments can be roughed out in OpticalRayTracer's virtual workbench.

optgeo

This is in french, but seems to fit some my requirements.

Both seem to be nice 2d tools, both are in the ubuntu repositories.

OpenRayTrace

From the manual:

OpenRayTrace is an optical lens design software that performs ray tracing. It is built using python, wxPython, and PyOpenGL. It should run on any platform that python, wxPython and PyOpenGL run on.

So it should in principle run on a linux box but I didn't manage to do so yet.

Here is a newer fork of the project: https://github.com/BenFrantzDale/OpenRayTrace

It also seems to support 3D ray tracing.

PyOptTools

pyOpTools is a set of packages that allow the simulation of optical systems by raytracing as well as some calculations involving wavefronts, currently under development. It is written in Python and Cython, and is being developed by the technological development group of Combustión Ingenieros S.A.S, and the applied optics group of the Universidad Nacional de Colombia.

A nice video of how it works can be found on youtube: https://www.youtube.com/watch?v=DB8sfm7pVPI

pyoptics

From the README:

Geometric optics raytracing in python for education and small-project design.

geoptics

From the documentation:

geoptics propagates light rays in 2D, in the geometrical optics approximation.

Modifying objects should be easy, with a live update of the rays propagation. The intent being to give a fun experience with optics.

That being said, physical precision is kept, so geoptics might interest engineers or physicists looking for a quick way to test ideas.

Still in alpha stage.

I am not aware of a simple program to do what you ask. What comes to mind are either raytracers or finite element methods (FEM).

For a list of raytracing software: http://en.wikipedia.org/wiki/List_of_ray_tracing_software

I am not aware of any free FEM software but for an overview of the principle go here: http://en.wikipedia.org/wiki/Finite_element

Edit: I didn't read carefully. You wanted geometrical optics. I was thinking of ray/wave optics.