Re: glass ...

[John Mallinckrodt <ajmallinckro@CSUPomona.Edu>]

On Tue, 27 May 1997, LUDWIK KOWALSKI wrote:

> Brian whatcott wrote:
>
> > One measures the angle A of the prism, and delta the angle of minimal 
> > deviation for a selected wavelength, and then the refractive index 
> > relative to air ( mu) is given by
> >
> >  mu = sin 1/2 (A + delta)/sin 1/2 A
>
> The trouble with this method is that the minimum is practically flat over
> the broad range of angles. Thus a very large uncertainty will always be
> associated with delta. I nice mathematical relation, but not very useful
> for measuring mu.

On the other hand, if the prism is equilateral, you can take advantage of
a very nice property of the internally reflected light to find the angle
of minimum deviation quite accurately.  In this case collimated incident
light of all wavelengths that suffers three (properly ordered) internal
reflections with the prism sides will emerge once again collimated.
Furthermore, the propagation direction is precisely that of noninternally
reflected light of the particular wavelength which happens to be at its
minimum deviation for the specific prism orientation. (Boy does the above
ever need a figure!)

The bottom line is that, if you can see the line due to the triply
internally reflected light (which will be composed of all wavelengths
present and, thus, have the same apparent color as the source), then all
you need to do is to rotate the prism until its line coincides with that
of the spectral component for which you desire to determine the angle of
minimum deviation.  When they coincide the spectral line of interest is
undergoing its minimum deviation and (since the prism is equilateral) the
formula above simplifies to

mu = cos(delta/2) + sqrt(3)*sin(delta/2)

John
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