A ray of light ravels from a liquid of refractive index `mu` to air. If the incident beam is rotating at a rate `omega` , what is the angular sped of the refracted beam at the instant the angle of incidence is `30^@` ? (Given ` mu=sqrt (2), omega =1//sqrt(6) rad s^(-1)`).

Explanation

To solve the problem step by step, we will analyze the situation involving the refraction of light from a liquid to air, using Snell's law and differentiation to find the angular speed of the refracted beam.

### Step 1: Understand the Setup
We have a ray of light traveling from a liquid with refractive index \( \mu \) to air. The incident angle \( \theta \) is given as \( 30^\circ \). We need to find the angular speed of the refracted beam when the incident beam is rotating at a rate \( \omega \).

### Step 2: Apply Snell's Law
Using Snell's law:
\[
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