Alayer of liquid b floats on liquid a. a ray of light begins in liquid a and undergoes total internal reflection at the interface between the liquids when the angle of incidence exceeds 38.0°. when liquid b is replaced with liquid c, total internal reflection occurs for angles of incidence greater than 49.5°. find the ratio nb/nc of the refractive indices of liquids b and c. nb/nc =?

The ratio of the refractive indices of the liquids is 1.22

Solution:

Critical angle for A and B interface,

Critical angle for A and B interface,

Now,

From the relation in between the critical angle and refractive index:

             (1)

where

n = rafractive index

= critical angle

Thus

For AB interface:

For AC interface:

Thus the ratio of the refractive indices of these liquids can be given as: