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Re: Angle of deviation



John Mallinckrodt wrote: "The only two answers I've seen so far suggest
that the angle of deviation is acute, but this is simply not so in
general; angles of deviation can be anything from 0 to 180 degrees.
(The text might have been clearer if it had said that the angle of
deviation is the angle between the *directions* of the incident and
emerging light rays.)"

I gave my answer (acute angle) because the text was specifically
refering to a prism. There is a formula that often appears in physics
texts for finding the refractive index of the material in a prism if you
know the angle of deviation and the angle of the prism corner. The
formula is:

n = (sin((d+p)/2))/sin(p/2)

where p is the angle of the corner of the prism being used, and d is the
minimum angle of deviation.

Note the word minimum. The prism must be adjusted so the angle of
deviation is at its minimum value. When this is true, the light path
through the prism corner is symmetric and the formula is not too hard to
derive.

When trying to use this formula I have seen people measure the wrong
angle because the wording in the text is not clear to many people. If
you draw the light path, and tell the person to measure the angle
between the incident ray and the refracted ray, they are likely to
measure the obtuse angle between the incoming ray and the outgoing ray,
because that is the only angle drawn on the paper. That is the wrong
angle to measure. I inferred from the question that this was the
situation being described, so that is the question I answered.

Measuring the angle between the incoming ray and the outgoing ray is
wrong in general if we are trying to find the "angle of deviation"
because the angle of deviation is indeed the angle between the
directions of the rays as John points out. And, as John said, adding
the word "directions" in the text would make it more clear. But a lot
of authors leave the word "directions" out because it is considered
superfluous, because that is how angles of deviation are supposed to be
measured. But it is only superfluous if you know it, and some people do
not know it.

Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton College
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.