Q42P - University Physics with Modern Physics

Question

A ray of light travelling in air is incident at angle ua on one face of a prism made of glass. Part of the light refracts into the prism and strikes the opposite face at point A (Fig. P33.42). If the ray at A is at the critical angle, what is the value of?

Step-by-Step Solution

Answer

the index of refraction is 1.305

the critical angle is 57.05°   

Step 1: About Critical angle

The critical angle is the angle of incidence where the angle of refraction is 90°. The light must travel from an optically more dense medium to an optically less dense medium.

Step 2 : Determine the index of refraction

We have the following prism with incident ray at an angle of 0“ from the normal to the prism surface. Since the prism is

having an angle of 90° at point c In triangle ABC A CBA would be 50° and A CAB would be 40°- 80 We can see that ray will

have an incidence angle of 50 ° at face AC. question is saying that at point A light is getting total internal re?ection so angle

after refraction Would be 90° -

Assume the index of refraction of prism equal to n- Apply the Snell's Law at point A-

 

 Therefore the index of refraction is 1.305

Step 3: Determine the Critical angle

Now we got the index of refraction of prism apply Snell's Law again at point B to get the value of 00-

Therefore the critical angle is 57.05°