Ordinary light incident on a glass slab at the polarising angle suffers a deviation of ` 22^(@)`. In this case, the angle of refraction is

Options

A. `56^@`
B. `34^(@)`
C. `68^(@)`
D. `22^@`

Explanation

To solve the problem of finding the angle of refraction when ordinary light is incident on a glass slab at the polarizing angle and suffers a deviation of 22 degrees, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Polarizing Angle**:
The polarizing angle (Brewster's angle) 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. This angle is given by the formula:
\[ \tan(\theta_p) = \frac{n_2}{n_1} \]
where \( \theta_p \) is the polarizing angle, \( n_1 \) is the refractive index of the first medium (air), and \( n_2 \) is the refractive index of the second medium (glass).

2. **Identify the Deviation**:
The problem states that the light suffers a deviation of 22 degrees. The deviation (\(\delta\)) can be expressed in terms of the angle of incidence (\(I\)) and the angle of refraction (\(R\)):
\[ \delta = I - R \]
Therefore, we can write:
\[ I - R = 22^\circ \]

3. **Use the Relationship of Angles**:
According to Brewster's law, at the polarizing angle, the angle of incidence and the angle of refraction are related as follows:
\[ I + R = 90^\circ \]
This means that the sum of the angle of incidence and the angle of refraction equals 90 degrees.

4. **Set Up the Equations**:
We now have two equations:
- \( I - R = 22^\circ \) (1)
- \( I + R = 90^\circ \) (2)

5. **Solve the Equations**:
We can solve these two equations simultaneously. From equation (2), we can express \(I\) in terms of \(R\):
\[ I = 90^\circ - R \]
Substitute this expression for \(I\) into equation (1):
\[ (90^\circ - R) - R = 22^\circ \]
Simplifying this gives:
\[ 90^\circ - 2R = 22^\circ \]
Rearranging this gives:
\[ 2R = 90^\circ - 22^\circ = 68^\circ \]
Therefore:
\[ R = \frac{68^\circ}{2} = 34^\circ \]

6. **Conclusion**:
The angle of refraction \(R\) when ordinary light is incident on a glass slab at the polarizing angle and suffers a deviation of 22 degrees is:
\[ R = 34^\circ \]