I have come up with an expression (for normal incidence) which relates these parameters, and which takes into account the multiple reflections between the top and bottom surfaces of a substrate:

T = 2n / (n^2 + 1),

where T is the Transmission and n is the Index.

If this is correct, then it follows that I can try to determine a value for n if I have measured T.

With a little manipulation I get that:

n = a + ((a^2 + 1)^0.5),

where a = 1/T.

My problem is, that while this works (more or less) for a CR39 lens, it does not work very well for higher index materials. I cannot, at the moment see why.

I have tried using plano lenses, but perhaps the surfaces are not exactly parallel, and some of the reflected light does not follow a predictable path.

Can anyone help, or suggest a more reliable method for finding the index of a material?