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...

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.