Question

A light ray enters a block of plastic and travels along the path shown.

a. By considering the behavior of the ray at point P, determine the speed of light in the plastic.

b. Determine what will happen to the light ray when it reaches point Q, using the diagram to illustrate your conclusion.

c. There is an air bubble in the plastic block that happens to be shaped like a plane-convex lens as shown below. Sketch what happens to parallel rays of light that strike this air bubble. Explain your reasoning.

Answer 1

(a) Note: The angles given are tricks. They are not measured from the normal, we must use the angle from normal.

Air → Plastic n_i sin θ_i = n_r sin θ_r, (1) sin (53) = n_r sin(37)  n_r = 1.33 

n = c /v 1.33 = 3x10⁸ / v

v = 2.26 x 10⁸ m/s

(b) Check the critical angle Plastic → Air. n_i sin θ_c = n_r sin (90) … (1.33) sin θ_c = (1) … θ_c = 48.75°

The incoming angle (53°) is larger than the critical angle, so total internal reflection will occur.

(c) This looks like a converging lens, but in lens problems, the lenses always have a higher index than the surrounding material. Since this ‘air lens’ has a smaller index of refraction it will behave the opposite as a normal lens would. From a simple refraction standpoint, there will be no refraction entering the air since the ray is perpendicular to the surface. Then on exiting, as you move less–more dense the ray bends towards the normal.