A ray moving in air at 62.9 deg
enters a plastic, where it bends to
52.8 deg. How fast does light
travel in the plastic?
(Hint: find n.)
(Water n = 1.33, Air n = 1.00)
(Answer is *10^8 m/s. Fill in the
number in the blank, not the power.)

The speed at which light travels in plastic is 2.68 * 10⁸ m/s.

Explanation:

Refractive index is the measure of the deflection of incident beam when it enters another medium. So depending upon the density of the medium, the refractive index will vary. From snell's law, the product of refractive index of the incident medium with the incident angle is equal to the product of refractive index of refracting medium with the refractive angle.

Since, here air is the incident medium and plastic is the refractive medium, the angle of incidence is given as 62.9 degree and the angle of refractance is given as 52.8 degree. It is known that the refractive index of air is 1. So the Snell's law is

Nₐ Sin θ₁ = N Sin θ₂

N = NₐSin θ₁/Sin θ₂

N = Sin 62.9/Sin 52.8 = 0.8902/0.7965

N=1.1176

Refractive index is also known as the measure of ratio of velocity of light in vacuum to velocity of light in any medium. Since we need to know the speed of ray moving in plastic medium, it can be found by ratio of speed of light in vacuum to refractive index of the medium.

N = c/v

velocity = c/N = 3*10⁸/1.1176 = 2.68 * 10⁸ m/s

So the speed at which light travels in plastic is 2.68 * 10⁸ m/s.