🚀 go-pugleaf

ACTIVITY 4  (another one with laser)
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Students familiar with programming and trigonometry may be asked to write a
program (or use a pocket calculator) to trace a laser beam through a prism.
This is accomplished by two consecutive applications of Snell's law, as
outlined below. The top angle of the prism, A, and the index of refraction
must be given. The task is to generate data for a plot of the deflection
angle (between the incoming and outgoing beams) versus the angle of incidence.
Then an experiment may be conducted to test predictions. Physics of refraction,
mathematics and programming come nicely together in one activity.

Another possibility, illustrated below, is to predict the dependence of the
angle of deflection on the index of refraction for a given angle of incidence,
for example 45 degrees. My results for that angle, and for a 60-degrees prism,
are shown below.

ind. of refr.    1.30   1.40   1.50   1.55   1.60   1.65   1.70
deflect (deg)   21.24  28.86  37.38  42.24  47.80  54.74  65.16

The index of refraction 1.72 resulted in the total internal reflection
on the second surface. You may ask students to measure the angle of
deflection and to use the above table to determine the index of refraction.
Laser beam deflection can be measured quite accurately in a large
classroom. Note that an error of about 2 degrees in the deflection angle
translates into an error of less than 0.02 in the index of refraction.
This shows that determinations of n can be quite accurate.

OUTLINE OF CALCULATIONS (from the optics textbook by Pederotti)
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Let TET1i be the angle of incidence on the first surface, A the prism angle,
and n the index of refraction. Then the angle of refraction after the first
surface, TET1r, can be found from Snell's law: 1*sin(TET1i)=n*sin(TET1r).
This in turn leads to the angle of incidence on the second surface, TET2i,
TET2i=A-TET1r. Use Snell's law again to find the angle of refraction after
the second surface: n*sin(TET2i)=1*sin(TET2r). That is it. The laser beam
going through the prism is deflected twice in the same direction. First by
TET1i-TET1r, on surface #1, then by TET2r-TET2i, on surface #2. The total
deflection angle is thus given by TET1i+TET2r-TET1r-TET2i.

           Trivial? Yes. Useful? I hope so. Ask for help if needed.


           Ludwik Kowalski         kowalski@apollo.montclair.edu