Two beam of red and violet colors are made to pass separately through a prism (angle of the prism is `60^(@)`). In the position of minimum deviation, the angle of refraction will be

Options

A. `30^(@)` for both the colors
B. greater for the violet color
C. greater for the red color
D. equal but not `30^(@)` for both the colors

Explanation

To solve the problem, we need to determine the angle of refraction for two beams of red and violet colors passing through a prism with an angle of 60 degrees at the position of minimum deviation.

### Step-by-Step Solution:

1. **Understanding the Prism and Minimum Deviation**:
- A prism is a transparent optical element with a defined geometry, typically made of glass or other materials. The angle of the prism is given as \( A = 60^\circ \).
- At the position of minimum deviation (\( D_{min} \)), the angle of incidence (\( i \)) is equal to the angle of emergence (\( e \)). Thus, \( i = e \).

2. **Using the Prism Formula**:
- The relationship between the angle of the prism, the angle of incidence, and the angle of refraction can be expressed using the prism formula:
\[ D_{min} = i + e - A \]
- Since \( i = e \), we can rewrite this as:
\[ D_{min} = 2i - A \]
- Rearranging gives us:
\[ 2i = D_{min} + A \quad \Rightarrow \quad i = \frac{D_{min} + A}{2} \]

3. **Finding the Angle of Refraction**:
- At minimum deviation, the light ray passes symmetrically through the prism. Therefore, the angle of refraction \( r \) at each face of the prism can be calculated using Snell's Law:
\[ n = \frac{\sin i}{\sin r} \]
- However, we also know that at minimum deviation, the angle of refraction \( r \) can be calculated as:
\[ r = \frac{A}{2} \]
- Substituting the value of \( A \):
\[ r = \frac{60^\circ}{2} = 30^\circ \]

4. **Conclusion**:
- The angle of refraction for both the red and violet beams at the position of minimum deviation through the prism is \( 30^\circ \).

### Final Answer:
The angle of refraction at the position of minimum deviation for both red and violet colors is \( 30^\circ \).