Question

A ray of light travels from an optically denser to rarer medium. The critical angle for the two media is $C.$ The maximum possible deviation of the ray will be

• A. $\frac{\pi }{2}-C$
• B. $2C$
• C. $\pi -2C$
• D. $\pi -C$

Answer 1

The correct option is C $\pi -2C$

Given: A ray of light travels from an optically denser to rarer medium. The critical angle for the two media is C.

To find the maximum possible deviation of the ray

Solution:

Critical angle is the angle of incidence for which the angle of refraction is $\frac{\pi }{2}$ for a given pair of media.

Let $\theta$ be the angle of incidence and $\varphi$ the angle of refraction.

When the ray passes from denser to rarer medium, the deviation is $\delta =\varphi -\theta$. If $\theta =C$ then $\varphi =\frac{\pi }{2}$ and deviation $\delta =\frac{\pi }{2}-C$. This is the maximum deviation. When total internal reflection occurs, the deviation is given by $\delta =\pi -2\theta$. Here $\delta$ is maximum when $\theta$ is minimum. The minimum value of $\theta$ is $C$.

Hence maximum deviation $\delta =\pi -2C$.