A ray of light-is incident on glass at the polarising angle ip. Find the angle between the reflected and refracted rays.

Answer

To solve the problem of finding the angle between the reflected and refracted rays when light is incident on glass at the polarizing angle \( i_p \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a ray of light incident on the interface between air and glass at the polarizing angle \( i_p \).
- At this angle, some light is reflected, and some is refracted.

2. **Applying Brewster's Law**:
- According to Brewster's Law, the polarizing angle \( i_p \) is related to the refractive index \( n \) of the glass by the equation:
\[ \tan(i_p) = n \]

3. **Applying Snell's Law**:
- Snell's Law relates the angles of incidence and refraction:
\[ \frac{\sin(i_p)}{\sin(r)} = n \]
- Here, \( r \) is the angle of refraction.

4. **Relating Angles**:
- From the geometry of the situation, we know that:
\[ i_p + r = 90^\circ \]
- This is because the angle of incidence and the angle of refraction add up to \( 90^\circ \) at the polarizing angle.

5. **Finding the Angle Between Reflected and Refracted Rays**:
- The angle of reflection is equal to the angle of incidence, so the angle of reflection is also \( i_p \).
- The angle between the reflected ray and the refracted ray can be calculated as:
\[ \text{Angle between reflected and refracted rays} = i_p + r \]
- Since \( i_p + r = 90^\circ \):
\[ \text{Angle between reflected and refracted rays} = 90^\circ \]

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

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