Given below are two statement : Statement I : If the Brewster`s angle for the light propagating from air to glass is `theta_B`,then the Brewster`s angle for the light propatingfrom glass to air is `pi/2-theta_B`. Statement II : The Brester`s ange for the light propageating from glass to air is `tan^(-1)(μ_g)` where `μ_g` is the refractive index of glass . In the light of above statement , choose the correct answer from the option given below:

Options

A. Both Statement I and Statement II are true
B. Both Statement I and Statement II are false
C. Statement I is true but Statement II is false
D. Statement I is false but Staement II is true

Answer

To solve the problem, we need to analyze both statements regarding Brewster's angle.

### Step-by-Step Solution:

1. **Understanding Brewster's Angle**:
Brewster's angle (θ_B) is the angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. The formula for Brewster's angle when light travels from medium 1 (with refractive index n1) to medium 2 (with refractive index n2) is given by:
\[ \tan(\theta_B) = \frac{n_2}{n_1} \]

2. **Analyzing Statement I**:
- The first statement claims that if the Brewster's angle for light propagating from air (n1 = 1) to glass (n2 = μ_g) is θ_B, then the Brewster's angle for light propagating from glass to air is \( \frac{\pi}{2} - \theta_B \).
- From the formula, we can derive that:
\[ \tan(\theta_B) = \frac{μ_g}{1} \implies θ_B = \tan^{-1}(μ_g) \]
- For light traveling from glass to air:
\[ \tan(\theta_2) = \frac{1}{μ_g} \implies θ_2 = \tan^{-1}\left(\frac{1}{μ_g}\right) \]
- Using the relation \( \theta_1 + \theta_2 = \frac{\pi}{2} \), we find:
\[ θ_2 = \frac{\pi}{2} - θ_B \]
- Therefore, Statement I is **True**.

3. **Analyzing Statement II**:
- The second statement claims that the Brewster's angle for light propagating from glass to air is \( \tan^{-1}(μ_g) \).
- As derived earlier, the Brewster's angle for light going from glass to air is actually:
\[ θ_2 = \tan^{-1}\left(\frac{1}{μ_g}\right) \]
- Thus, Statement II is **False** since it incorrectly states that \( θ_2 = \tan^{-1}(μ_g) \).

4. **Conclusion**:
- Statement I is True.
- Statement II is False.
- Therefore, the correct answer is that Statement I is true and Statement II is false.

### Final Answer:
- Statement I is True, Statement II is False.