Question

The Brewster angle for air to glass transition of light is 
(Refractive index of glass = $1.5$

• A. $\sin^{-1} \left(\frac{3}{2}\right)$
• B. $\cos^{-1} \left(\frac{3}{2}\right)$
• C. $\tan^{-1} \left(\frac{3}{2}\right)$
• D. $\cos^{-1} \left(\frac{2}{3}\right)$

Hint:

Brewster's angle $\theta_B$ is given by $\tan \theta_B = n$. For air-to-glass transition, where $n = 1.5$, we use $\theta_B = \tan^{-1} (1.5)$.

Answer 1

The Correct Option is C

Step 1: Understanding Brewster's Law 
Brewster's angle $\theta_B$ is the angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface without any reflection. It is given by: $$\tan \theta_B = n$$ where $n$ is the refractive index of the second medium (glass) concerning the first medium (air). 

Step 2: Apply the given values 
Given $n = 1.5$, the Brewster angle is: $$\theta_B = \tan^{-1} (n)$$ $$\theta_B = \tan^{-1} \left(\frac{3}{2}\right)$$ 

Step 3: Identify the correct option 
From the given answer choices, the correct expression is: $$\tan^{-1} \left(\frac{3}{2}\right)$$ Thus, the correct answer is Option (3).