From dave@onfcanim.UUCP Thu Feb  2 19:53:14 1989
Path: leah!csd4.milw.wisc.edu!mailrus!jarvis.csri.toronto.edu!utgpu!watmath!onfcanim!dave
From: dave@onfcanim.UUCP (Dave Martindale)
Newsgroups: comp.graphics
Subject: Re: Ray tracing refraction
Message-ID: <17363@onfcanim.UUCP>
Date: 3 Feb 89 00:53:14 GMT
References: <0XryqWy00Uo1875Ud-@andrew.cmu.edu> <101880003@hpcvlx.HP.COM> <49391@yale-celray.yale.UUCP>
Reply-To: dave@onfcanim.UUCP (Dave Martindale)
Organization: National Film Board / Office national du film, Montreal
Lines: 42

In article <101880003@hpcvlx.HP.COM> tomg@hpcvlx.HP.COM (Thomas J. Gilg) writes:
>Question : is the index of refraction linear with repect to the
>wavelength ?  I started writting a ray tracer and took liberty in
>assuming linear response.  Any experts out there ?

I'm far from an expert.  However, I do know that at least some optical design
is done using a polynomial model of refractive index (n) as a function
of wavelength (w) (my terminal doesn't do lambda!).

The polynomial is:  n**2 = A0 + A1 * w**2 + A2 * w**(-2) + A3 * w**(-4)

			+ A4 * w**(-6) + A5 * w**(-8)

Note that the polynomial doesn't give you n, but n squared.  

The glass manufacturer gives you A0 through A5.  For BK 7, a commonly-used
crown glass, the constants are:

	A0	 2.2718929
	A1	-1.0108077e-2
	A2	 1.0592509e-2
	A3	 2.0816965e-4
	A4	-7.6472538e-6
	A5	 4.9240991e-7

These constants are applicable when the wavelength w is in microns.
For other units of W, scale the constants appropriately.

The wavelength of green light is 0.55 microns; substituting that into
the formula will quickly show which of the terms are insignificant for
your purposes.

I've also seen formulas for the refractive index of synthetic fused silica
and for saphhire, and they are *not* polynomials.  So if you're going to
be general about modelling refractive index, you probably have to allow
for an arbitrary function, not just a polynomial.

By the way, does anyone have a ray-tracer that is intended for optical
design rather than producing pictures?  Are you willing to give it away?
If so, I want it!

	Dave Martindale