An upolarized light beam is incident on a surface at an angle of incidence equal to Brewster's angle. Then,

Options

A. the reflected and the refracted beam are both partially polarized
B. the reflected beam is partially polarized and the refracted beam is completely polarized and are at right angles to each other
C. the reflected beam is completely polarized and the refracted beam is partially polarized and are at right angles to each other
D. both the reflected and the refracted beams are completely polarized and are at right angles to each other.

Answer

To solve the problem regarding the behavior of an unpolarized light beam incident on a surface at Brewster's angle, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Brewster's Angle**:
Brewster's angle (θ_B) is defined as the angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. It can be calculated using the formula:
\[ \tan(\theta_B) = \frac{n_2}{n_1} \]
where \( n_1 \) is the refractive index of the first medium (usually air) and \( n_2 \) is the refractive index of the second medium.

2. **Incident Light Characteristics**:
The light beam incident on the surface is unpolarized. Unpolarized light consists of waves vibrating in multiple planes.

3. **Behavior of Light at Brewster's Angle**:
When unpolarized light strikes the surface at Brewster's angle:
- The reflected light is completely polarized.
- The refracted light is partially polarized.

4. **Angle Relationships**:
At Brewster's angle, the reflected and refracted rays are perpendicular to each other. This means:
\[ \theta_B + \theta_r = 90^\circ \]
where \( \theta_r \) is the angle of refraction.

5. **Conclusion**:
Therefore, when unpolarized light is incident at Brewster's angle:
- The reflected beam is completely polarized.
- The refracted beam is partially polarized.
- The reflected and refracted beams are at right angles to each other.

### Final Answer:
The correct statement is:
- The reflected beam is completely polarized, and the refracted beam is partially polarized. Both beams are at right angles to each other.

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