A prism has a refracting angle of `60^@` . When placed in the position of minimumm deviation, it produces a deviation of 30°. The angle of incidence is,

Options

A. 30°
B. 45°
C. 15°
D. 60°

Explanation

To solve the problem, we need to find the angle of incidence (i) for a prism with a refracting angle (A) of 60° that produces a minimum deviation (δ) of 30°.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Refracting angle of the prism, A = 60°
- Angle of minimum deviation, δ = 30°

2. **Use the Formula for Minimum Deviation:**
In the case of minimum deviation, the relationship between the angle of incidence (i), angle of refraction (r), and the refracting angle (A) can be expressed as:
\[ i + r = A + δ \]

3. **At Minimum Deviation:**
When the prism is in the position of minimum deviation, the angle of incidence (i) is equal to the angle of emergence (e), and the angle of refraction (r) is equal to half the refracting angle:
\[ r = \frac{A}{2} = \frac{60°}{2} = 30° \]

4. **Substituting Values:**
Now, substituting the values into the equation:
\[ i + r = A + δ \]
\[ i + 30° = 60° + 30° \]
\[ i + 30° = 90° \]

5. **Solve for Angle of Incidence (i):**
Rearranging the equation to find i:
\[ i = 90° - 30° \]
\[ i = 60° \]

### Final Answer:
The angle of incidence (i) is **60°**.