A ray of light in air is incident on a glass plate at polarising angle of incidence. It suffers a deviations of `22^(@)` on entering glass. The angle of polarisation is

Options

A. `90^(@)`
B. `56^(@)`
C. `68^(@)`
D. zero

Answer

To solve the problem, we need to determine the angle of polarization (i) when a ray of light in air is incident on a glass plate at the polarizing angle of incidence, which results in a deviation of 22 degrees upon entering the glass.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- A ray of light is incident on a glass plate at the polarizing angle of incidence.
- The deviation of the ray upon entering the glass is given as 22 degrees.
- We need to find the angle of polarization.

2. **Using Snell's Law**:
- According to Snell's Law, we have:
\[ \frac{\sin i}{\sin r} = \mu \]
where \( i \) is the angle of incidence, \( r \) is the angle of refraction, and \( \mu \) is the refractive index of glass.

3. **Relating the Angles**:
- The angle of refraction \( r \) can be expressed in terms of the angle of incidence \( i \) and the deviation:
\[ r = i - 22^\circ \]

4. **Substituting in Snell's Law**:
- Substitute \( r \) into Snell's Law:
\[ \frac{\sin i}{\sin(i - 22^\circ)} = \mu \]

5. **Polarizing Angle Relation**:
- At the polarizing angle, the refractive index \( \mu \) can also be expressed as:
\[ \mu = \tan i \]
- Therefore, we can rewrite Snell's Law as:
\[ \frac{\sin i}{\sin(i - 22^\circ)} = \tan i \]

6. **Using Trigonometric Identity**:
- We know that:
\[ \tan i = \frac{\sin i}{\cos i} \]
- Thus, we can rewrite the equation:
\[ \frac{\sin i}{\sin(i - 22^\circ)} = \frac{\sin i}{\cos i} \]

7. **Cross Multiplying**:
- Cross-multiplying gives:
\[ \sin i \cdot \cos i = \sin(i) \cdot \sin(i - 22^\circ) \]

8. **Using Sine Addition Formula**:
- Using the identity \( \sin(a - b) = \sin a \cos b - \cos a \sin b \):
\[ \sin(i - 22^\circ) = \sin i \cos 22^\circ - \cos i \sin 22^\circ \]

9. **Setting the Equation**:
- Substitute this back into the equation:
\[ \sin i \cdot \cos i = \sin i (\sin i \cos 22^\circ - \cos i \sin 22^\circ) \]

10. **Solving for i**:
- After simplification, we find:
\[ 90 - i = i - 22 \]
\[ 90 + 22 = 2i \]
\[ 112 = 2i \implies i = \frac{112}{2} = 56^\circ \]

11. **Conclusion**:
- The angle of polarization is \( 56^\circ \).

### Final Answer:
The angle of polarization is \( 56^\circ \).