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Trapezoidal Slab: Internal and External Incidence

1. Trace an outline of the trapezoidal slab, and use pins to define an incident ray.  Use an incident angle greater than 30 degrees to avoid excessive error (why?). 
2. While sighting through the glass, position two more pins so that they appear to line up with those placed in Step 1.  Use a protractor to carefully measure the incident and transmitted angle for external incidence (θ_i and θ_t) and those for internal incidence (θ'_i and θ'_t).
3. Use Snell's law to determine values for the index of refraction using data for both external and internal incidence.  Compare your two values with a percent difference.

Note:  you can look through the slab in either direction.  If they appear to be aligned in one direction, they will appear aligned when observed from the opposite direction.  Try it!

Semicircular Slab:  External Incidence

Trace an outline of the semicircular slab, and use pins to define an incident ray.  You will be tracing three different rays, so try for one between 30 and 40 degrees, followed by one between 40 and 50 degrees, followed by one between 50 and 60 degrees.  For each case, sight through the slab, and position a third pin so that it lines up with the first two.  Apply Snell's law at the flat surface to determine three different values for the index of refraction.  Average the three values.

Note:  try your best to make sure that the pin adjacent to the flat surface is located precisely at the center point of the circular surface.  Only then will the refracted ray travel along a radius line for normal incidence at the curved surface.  This avoids additional refraction as the ray exits the slab.

Note:  in this case, you really need to observe along the ray that encounters the straight side first (i.e., from the lower left in the figure above).  In principle, it should work fine from the opposite direction, but the curved side acts like a cylindrical lens, and distorts your view of the other two pins.

Semicircular Slab:  Total Internal Reflection

Reverse the semicircular piece of glass, trace it, and make sure that a pin is located and the center point.  Now sight through the curved side of the slab.   Position the second pin precisely at the point where the first pin disappears.  The two pins now define the critical angle for total internal reflection.  Use the formula for the critical angle to determine another value for the index of refraction, and compare to the average obtained above with a percent difference.