A scientist holds a thin section of unknown material mounted on glass (n=1.520) and shines a laser through the glass toward the bottom of the unknown material while looking at it from above. The laser is labeled as emitting light of 640 nm, which is the wavelength the light has when traveling through air. The scientist begins by aiming the laser along the normal and then slowly increases the angle of incidence just enough for total internal reflection to begin occurring at the interface of the unknown material and the air. At that point, the angle of the light relative to the normal while in the glass is ?1 and once the light moves into the unknown medium, the angle of the light relative to the normal is 31.0.

a) Find ?1. _______________________

b) What is the index of refraction of the unknown material? _______________________

c) What is the speed of light in the unknown material? _______________________

d) What is the frequency of the laser light in the unknown material? _______________________

S air n=1.0003 ?? ? D glass n=1.520