A ray of light passes through the equilateral prism such that angle of incidence is equal to the angle of emergence if the angle of incidence is `45^(@)`. The angle of deviation will be

Options

A. `15^@`
B. `75^@`
C. `60^@`
D. `30^@`

Answer

To find the angle of deviation for a ray of light passing through an equilateral prism with an angle of incidence equal to the angle of emergence, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information**:
- Angle of incidence (i) = 45°
- Angle of emergence (e) = 45° (since it is given that angle of incidence is equal to angle of emergence)
- Angle of the prism (A) = 60° (for an equilateral prism)

2. **Understand the Concept of Minimum Deviation**:
- When the angle of incidence is equal to the angle of emergence, it indicates that the light ray is undergoing minimum deviation.

3. **Use the Formula for Angle of Deviation**:
- The formula for the angle of deviation (Δ) in terms of the angle of incidence (i), angle of emergence (e), and angle of the prism (A) is given by:
\[ Δ + A = i + e \]

4. **Substitute the Known Values into the Formula**:
- Substitute A = 60°, i = 45°, and e = 45° into the equation:
\[ Δ + 60° = 45° + 45° \]

5. **Calculate the Right Side**:
- Calculate the sum on the right side:
\[ Δ + 60° = 90° \]

6. **Isolate the Angle of Deviation (Δ)**:
- Rearranging the equation to solve for Δ:
\[ Δ = 90° - 60° \]

7. **Final Calculation**:
- Calculate Δ:
\[ Δ = 30° \]

### Conclusion:
The angle of deviation (Δ) is **30°**.