If the angle of prism is `60^(@)` and the angle of minimum deviaton 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 given the angle of the prism and the angle of minimum deviation, we can use the formula for the refractive index (μ) in terms of the prism angle (A) and the angle of minimum deviation (D).

### Step-by-Step Solution:

1. **Identify the given values:**
- Angle of prism (A) = 60°
- Angle of minimum deviation (D) = 40°

2. **Use the formula for the refractive index (μ):**
\[ \mu = \frac{\sin\left(\frac{A + D}{2}\right)}{\sin\left(\frac{A}{2}\right)} \]

3. **Calculate A + D:**
\[ A + D = 60° + 40° = 100° \]

4. **Calculate \(\frac{A + D}{2}\):**
\[ \frac{A + D}{2} = \frac{100°}{2} = 50° \]

5. **Calculate \(\frac{A}{2}\):**
\[ \frac{A}{2} = \frac{60°}{2} = 30° \]

6. **Substitute the values into the refractive index formula:**
\[ \mu = \frac{\sin(50°)}{\sin(30°)} \]

7. **Recall that \(\sin(30°) = \frac{1}{2}\):**
\[ \mu = \frac{\sin(50°)}{\frac{1}{2}} = 2 \cdot \sin(50°) \]

8. **Calculate \(\sin(50°)\):**
- Using a calculator or trigonometric table, \(\sin(50°) \approx 0.766\).

9. **Now calculate μ:**
\[ \mu = 2 \cdot 0.766 \approx 1.532 \]

10. **Conclusion:**
The refractive index (μ) is approximately 1.53.