1 b) Even though the lab sheet has Snel's Law as n = sin theta 1/sin theta 2 this is true only when medium 1 is a vacuum or a diffuse gas such as room pressure air. The correct formulation comes from the fact that sines are proportional to the velocities so that
sin theta 1/sin theta 2 = c1/c2 = n2/n1.
2) The critical angle occurs when light in the denser medium totally reflects off the interface with a less dense medium. The critical angle is when the light trying to enter the less dense medium bending away from the normal bends to an angle of 90 deg from the normal. Thus sin theta less dense = 1 since sin 90 = 1. Using results from above we have
sin theta more dense/sin theta less dense = n less/ n more or
sin theta critical /1 = nless/nmore
which also gives n more = nless/ sin theta critical
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