Question

Select the correct statement.

• A. If the Brewster's angle for the light propagation from air to glass is '$\theta$', then Brewster's angle for the light propagating from glass to air is $(\frac{\pi}{2} - \theta)$.
• B. The Brewster's angle for the light propagating from the glass to air is $\tan^{-1}(\mu)$ where $\mu$ is the refractive index of glass.
• C. The Brewster's angle for light propagating from air to glass is '$\theta$' then Brewster's angle for the light propagating from glass to air is $(\pi + \theta)$.
• D. The Brewster's angle for light propagating from glass to air is $\tan(\mu)$ where $\mu$ is the refractive index of glass.

Hint:

At Brewster's angle, the reflected and refracted rays are perpendicular to each other.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
Brewster's Law states that for a specific angle of incidence (Brewster's angle), the reflected light is completely polarized. The relationship depends on the refractive indices of the two media.
Step 2: Key Formula or Approach:
Brewster's angle $\theta_p$ is given by:
\[ \tan \theta_p = \frac{\mu_2}{\mu_1} \]
where $\mu_2$ is the refractive index of the second medium and $\mu_1$ is the first.
Step 3: Detailed Explanation:
For propagation from air to glass:
Let the refractive index of glass be $\mu$. For air, $\mu_{air} = 1$.
\[ \tan \theta = \frac{\mu}{1} \implies \tan \theta = \mu \]
For propagation from glass to air:
Let the new Brewster's angle be $\theta'$.
\[ \tan \theta' = \frac{1}{\mu} \]
Substituting $\mu = \tan \theta$:
\[ \tan \theta' = \frac{1}{\tan \theta} = \cot \theta \]
Using trigonometric identity $\cot \theta = \tan(\frac{\pi}{2} - \theta)$:
\[ \tan \theta' = \tan\left(\frac{\pi}{2} - \theta\right) \]
Thus, $\theta' = \frac{\pi}{2} - \theta$.
Step 4: Final Answer:
Statement (A) is correct as it accurately reflects the mathematical relationship between the two Brewster angles.