Question

A glass is half-full of water, with a layer of vegetable oil (n 5 1.47) fl oating on top. a ray of light traveling downward through the oil is incident on the water at an angle of 71.48. determine the critical angle for the oil–water interface and decide whether the ray will penetrate into the water.

Answer 1

The critical angle is the angle of incidence which gives 90 degrees refraction of light. If the incident angle is less than the critical angle, the ray of light will penetrate the second medium and if the incident angle is more than the critical angle, the ray will not penetrate and total internal reflection will occur.

So, to decide whether the ray will penetrate or not, we need to calculate the critical angle and compare it with the incident angle.

critical angle is calculated using the following rule:
critical angle = arcsin (n2 / n1) where
n1 is that of the oil = 1.47
n2 is that of the water = 1.33
therefore,
critical angle =  arcsin (1.33 / 1.47) = 64.79 degree

Since the incident angle is greater than the critical angle, therefore the ray will not penetrate and will undergo total internal reflection.