A ray of light is incident on the surface of a glass plate at an angle of incidence equal to Brewster's angle `phi`. If `mu` represents the refractive index of glass with respect to air, then the angle between reflected and refracted rays is

Options

A. `90 + omega`
B. `sin^(-1)(mucosphi)`
C. `90^@`
D. `90^@-sin^(-1)(sinphi//mu)`

Answer

To solve the problem, we need to understand the relationship between the angles of incidence, reflection, and refraction at Brewster's angle.

### Step-by-Step Solution:

1. **Understanding Brewster's Angle**:
Brewster's angle (φ) 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. At this angle, the reflected and refracted rays are perpendicular to each other.

2. **Using Snell's Law**:
According to Snell's law, the relationship between the angles of incidence (i), reflection (r), and refraction (t) is given by:
\[ n_1 \sin(i) = n_2 \sin(t) \]
Where \( n_1 \) is the refractive index of the first medium (air, approximately 1), and \( n_2 \) is the refractive index of the second medium (glass, represented as μ).

3. **Brewster's Angle Relation**:
At Brewster's angle, the following relationship holds:
\[ \tan(\phi) = \frac{n_2}{n_1} = \mu \]
This means that the angle of refraction (t) can be expressed as:
\[ t = 90^\circ - \phi \]

4. **Finding the Angle Between Reflected and Refracted Rays**:
The angle between the reflected ray and the refracted ray can be calculated as follows:
- The angle of reflection (r) is equal to the angle of incidence (i), which is φ.
- The angle of refraction (t) is \( 90^\circ - \phi \).

Therefore, the angle between the reflected ray and the refracted ray is:
\[ \text{Angle} = r + t = \phi + (90^\circ - \phi) = 90^\circ \]

5. **Conclusion**:
The angle between the reflected and refracted rays is \( 90^\circ \).

### Final Answer:
The angle between the reflected and refracted rays is \( 90^\circ \).

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