Question

The polarising angle for a transparent medium is \( \theta \) and \( v \) is the speed of light in that medium, then relation between \( \theta \) and \( v \) is (c = velocity of light)

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

Hint:

Brewster's Law helps us find the polarising angle by relating it to the refractive index, which is the ratio of the speed of light in vacuum to the speed of light in the medium.

Answer 1

The Correct Option is C

Step 1: Understanding the polarising angle.
The polarising angle \( \theta \) is related to the refractive index \( n \) by the Brewster's Law, which states that \( \tan \theta = n \). The refractive index is also related to the speed of light in different mediums by the formula \( n = \frac{c}{v} \), where \( c \) is the speed of light in vacuum and \( v \) is the speed in the medium.
Step 2: Deriving the formula.
By substituting the refractive index \( n = \frac{c}{v} \) into Brewster's Law, we get: \[ \tan \theta = \frac{c}{v} \Rightarrow \theta = \cot^{-1} \left( \frac{v}{c} \right) \] Step 3: Conclusion.
Thus, the correct relation is \( \theta = \cot^{-1} \left( \frac{v}{c} \right) \), which corresponds to option (C).