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

enter image description here

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:enter image description here

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?

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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.

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  • $\begingroup$ the cited tutorial doesn't even leave a word on the determinant of the ray matrix. $\endgroup$ – Quantumwhisp Dec 4 '16 at 23:38

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