Question

A light ray enters a glass enclosed fish tank. From air it enters the glass at 20° with respect to the plane of the surface and then emerges into the water. The index for the glass is 1.50 and for water 1.33.

(a) What is the angle of refraction in the glass?

(b) What is the angle of refraction in the water?

(c) Is there any incident angle in air for which the ray will not enter the water due to total internal reflection? If so, find it.

Answer 1

(c) No

Use Snell's law and the data you have. First, look at the air-glass interface. na = index of air = 1, ng = index of glass. Then

na*sin(qa) = nw*sin(qg) where qa, qg are angles of incidence/refraction for air and glass respectively

If there is total internal reflection at this interface then sin(qg) = 1 --> qg = 90 deg so

sin(qa) = nng/na = 1.5 but clearly -1< = sin(x) <= 1 so there is no angle at this interface that causes total internal reflection.

Now look at glass water interface

ng*sin(qg) = nw*sin(qw) and set qw = 90 deg ---> sin(qg) = nw/ng = 1.33/1.5 = 0.887

so qg = 62.46 deg.

Now play this back through the air-glass interface

sin(qa) = ng*sin(qg) = 1.33 --> therefore, there is no incident angle where you can get total internal reflection