Light in air is incident on a plastic plate at the Brewster angle. The angle of refraction is `35.0^(@)`
Determine the Brewster angle.

Options

A. `35.0^(@)`
B. `46.5^(@)`
C. `55.0^(@)`
D. `43.5^(@)`

Answer

To determine the Brewster angle when light in air is incident on a plastic plate at the Brewster angle with a given angle of refraction of 35 degrees, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Brewster's Angle**: Brewster's angle (denoted as \( \theta_B \)) is the angle of incidence at which the reflected and refracted rays are perpendicular to each other. This means that the angle between the reflected ray and the refracted ray is 90 degrees.

2. **Identify Given Information**:
- The angle of refraction \( \theta_r = 35^\circ \).

3. **Calculate the Angle of Reflection**:
- According to the law of reflection, the angle of reflection \( \theta_r \) is equal to the angle of incidence \( \theta_i \) when light reflects off a surface.
- Since the reflected ray and the refracted ray are at 90 degrees to each other, we can express this relationship as:
\[ \theta_r + \theta_i = 90^\circ \]
- Rearranging this gives us:
\[ \theta_i = 90^\circ - \theta_r \]

4. **Substitute the Angle of Refraction**:
- Now substitute \( \theta_r = 35^\circ \) into the equation:
\[ \theta_i = 90^\circ - 35^\circ = 55^\circ \]

5. **Conclusion**:
- The Brewster angle \( \theta_B \) is equal to the angle of incidence \( \theta_i \) when light is incident at Brewster's angle. Thus, we find:
\[ \theta_B = 55^\circ \]

### Final Answer:
The Brewster angle is \( 55^\circ \).

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