refraction

The refractive index is defined as the ratio of the speed of light in a vacuum to the speed of light in a medium (in this case, plastic). So, to solve part a, you are given that 1.52 = speed of light in vacuum / speed of light in plastic. The speed of light in a vacuum is a known constant that you should have in your class notes.

Definition of critical angle: if light strikes a surface with an incident angle higher than the critical angle, the light is only able to be reflected (not refracted). The critical angle is related to the index of refraction by the equation: sin (critical angle) = 1/n

Finally, for part c, you need to use a variation of Snell's law:
n1 sin(theta1) = n2 sin(theta2)
You are given "theta1", the angle of the laser in air, and "n2", the refractive index of the plastic. The refractive index of air ("n1") at 15 oC is 1.00028 (could be approximated as 1.0); solve for "theta2".