What is the speed of light in plastic?
Light traveling in air is incident on the surface of a block of plastic at an angle of 72.7° to the normal and is bent so that it makes a 57.1° angle with the normal in the plastic. Find the speed of light in the plastic.
Snell's law is the relation that describes the relationship between the angles of incidence and refraction, with respect to light waves passing through a boundary, such as air and plastic. The law states that the ratio of the sines of the angles of incidence and of refraction is a constant :
n1 sin(t1) = n2 sin(t2)
where n1 and n2 are the refractive indices.
The refractive index is one measure of the speed of light in a material, being defined as the ratio of the speed of light in vacuum relative to that in the considered medium. In your question, the speed of light in air is approcimately that in vacuum, thus n1 = c / c = 1, where c is the speed of light. n2 = c / v, where v is the speed of light in the plastic.
Substituting into Snell's law,
1 sin(72.7) = c / v sin(57.1)
v = c sin(57.1) / sin(72.7)
v = 0.88 c, or 88% the speed of light.