A ray of light is incident on a medium boundry at polarising angle such that its deviation is `24^(@)`, then angle of incidence is :

Options

A. `78^(@)`
B. `57^(@)`
C. `66^(@)`
D. `90^(@)`

Answer

To solve the problem, we need to find the angle of incidence (ip) when a ray of light is incident at the polarizing angle, and the deviation (δ) is given as 24 degrees.

### Step-by-step Solution:

1. **Understanding the Setup**:
- When light is incident at the polarizing angle, it undergoes refraction. The angle of incidence is denoted as \( ip \), the angle of refraction as \( r \), and the deviation as \( \delta \).

2. **Relating Angles**:
- The deviation \( \delta \) is defined as the difference between the angle of incidence and the angle of refraction:
\[ ip = r + \delta \]
- Given \( \delta = 24^\circ \), we can rewrite this as:
\[ ip = r + 24^\circ \quad \text{(Equation 1)} \]

3. **Using the Sum of Angles**:
- According to the laws of optics, the sum of the angle of incidence and the angle of refraction at the boundary is:
\[ ip + r = 90^\circ \quad \text{(Equation 2)} \]

4. **Substituting Equation 1 into Equation 2**:
- We can substitute \( r \) from Equation 1 into Equation 2. From Equation 1, we can express \( r \) as:
\[ r = ip - 24^\circ \]
- Now substituting this into Equation 2:
\[ ip + (ip - 24^\circ) = 90^\circ \]
- This simplifies to:
\[ 2ip - 24^\circ = 90^\circ \]

5. **Solving for \( ip \)**:
- Adding \( 24^\circ \) to both sides gives:
\[ 2ip = 90^\circ + 24^\circ \]
\[ 2ip = 114^\circ \]
- Dividing both sides by 2 results in:
\[ ip = 57^\circ \]

### Final Answer:
The angle of incidence \( ip \) is \( 57^\circ \).

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