Question

The polarising angle of transparent medium is $\theta$. Let the speed of light in the medium be $v$. Then the relation between $\theta$ and $v$ is ($c=$ velocity of light in air)

• A. $\theta=\sin^{-1}(v/c)$
• B. $\theta=\tan^{-1}(v/c)$
• C. $\theta=\cot^{-1}(v/c)$
• D. $\theta=\cos^{-1}(v/c)$

Hint:

Brewster's angle depends on the refractive index of the interface.

Answer 1

The Correct Option is C

Step 1: Formula
By Brewster's Law, $\mu = \tan \theta$, where $\theta$ is the polarizing angle.

Step 2: Analysis
The refractive index $\mu$ is also defined as $\mu = c/v$.
So, $\tan \theta = c/v$.

Step 3: Calculation
If $\tan \theta = c/v$, then $\cot \theta = v/c$.
Therefore, $\theta = \cot^{-1}(v/c)$.

Step 4: Conclusion
Hence, the relation is $\theta=\cot^{-1}(v/c)$. Final Answer: (C)