Determinant of ray transfer matrix

Question

Quick question on the wikipedia entry for the ray transfer matrix, which is defined :

where $x$ is the distance of a point from the optical axis and $\theta$ the angle that the beam profile at that point makes with the optical axis.

Now, wikipedia says:

but does NOT provide a reference.

Does anyone have any idea on how to get that results? Do you know a website/paper where this is discussed?

Answer 1

I don't know why they say a thermodynamics argument is needed. Here is a tutorial on basic optical design that shows it from Snell's law and simple geometry.