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

Options

A. `30degree` for both the colours
B. greater for the violet colour
C. greater for the red colour
D. equal but not `30degree` for both the colours

Explanation

To solve the problem, we need to determine the angle of refraction for both the red and violet beams of light 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 bends light due to refraction. The angle of the prism is given as 60 degrees.
- The position of minimum deviation occurs when the light rays pass symmetrically through the prism, meaning the angle of incidence equals the angle of emergence.

2. **Applying Snell's Law**:
- Snell's Law states that \( n_1 \sin(i) = n_2 \sin(r) \), where \( n_1 \) and \( n_2 \) are the refractive indices of the mediums, \( i \) is the angle of incidence, and \( r \) is the angle of refraction.
- In the case of minimum deviation, the light enters and exits the prism at the same angle of incidence and angle of emergence.

3. **Calculating the Angles**:
- For a prism, the relationship between the angle of the prism \( A \), the angle of incidence \( i \), and the angle of refraction \( r \) can be expressed as:
\[ i + r = A + D \]
where \( D \) is the angle of deviation.
- At minimum deviation, the angle of deviation \( D \) is minimized, and the relationship simplifies.

4. **Finding the Angle of Refraction**:
- Since the prism angle \( A \) is 60 degrees, we can express the relationship as:
\[ i + r = 60^\circ + D_{min} \]
- At minimum deviation, the angle of incidence \( i \) equals the angle of emergence, and thus:
\[ 2r = 60^\circ + D_{min} \]
- For the case of minimum deviation, we can assume \( D_{min} \) to be a small angle, which allows us to approximate:
\[ 2r = 60^\circ \]
- Therefore, solving for \( r \):
\[ r = \frac{60^\circ}{2} = 30^\circ \]

5. **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 will be \( 30^\circ \) for both the red and violet beams.