Question

A ray of light travelling in a transparent medium of refractive index µ, falls on a surface separating the medium from air at an angle of incidence of 45º. For which of the following value of µ the ray can undergo total internal reflection -

Answer 1

The ray can undergo total internal reflection for values of $\mu$ > √2 .

Given a ray of light travelling in a transparent medium of refractive index µ, falls on a surface separating the medium from air at an angle of incidence of 45º.

• Angle of incidence = i = 45°
• Critical angle , C = 1/$\mu$  

For total internal refraction to occur,

• Angle of incidence > Critical Angle .
• i > c
• sin i > sin c

Therefore,

• Sin 45° > 1/$\mu$  
• 1/√2 > 1/$\mu$
• $\mu$ > √2

Therefore we have seen the value of $\mu$ for the light ray to undergo total internal reflection is $\mu$ > √2