If the angle of prism is `60^(@)` and the angle of minimum deviation is `40^(@)` , the angle of refraction will be

Options

A. `30^@`
B. `60^@`
C. `100^@`
D. `120^@`

Answer

To find the angle of refraction when the angle of prism \( A \) is \( 60^\circ \) and the angle of minimum deviation \( D_m \) is \( 40^\circ \), we can use the relationship between the angle of prism and the angle of refraction at minimum deviation.

### Step-by-Step Solution:

1. **Understand the relationship**: In the case of minimum deviation, the angle of prism \( A \) is related to the angle of refraction \( r \) by the formula:
\[ A = 2r \]
This means that when the light passes through the prism at the angle of minimum deviation, the angle of refraction on both sides of the prism is equal.

2. **Substitute the given values**: We know the angle of prism \( A = 60^\circ \). Plugging this into the formula gives:
\[ 60^\circ = 2r \]

3. **Solve for \( r \)**: To find \( r \), divide both sides of the equation by 2:
\[ r = \frac{60^\circ}{2} = 30^\circ \]

4. **Conclusion**: The angle of refraction \( r \) is \( 30^\circ \).

### Final Answer:
The angle of refraction is \( 30^\circ \).