The minimum deviation produced by a glass prism of angle `40^(@)` is `36^(@)`. The refractive index of the glass will be

Options

A. 1.4
B. 1.2
C. 1.5
D. 1.8

Explanation

To find the refractive index of the glass prism given the angle of the prism and the minimum deviation, we can use the formula for the refractive index (μ) of a prism:

\[ \mu = \frac{\sin\left(\frac{A + D_m}{2}\right)}{\sin\left(\frac{A}{2}\right)} \]

Where:
- \( A \) is the angle of the prism,
- \( D_m \) is the minimum deviation.

### Step-by-Step Solution:

1. **Identify the given values:**
- Angle of the prism, \( A = 40^\circ \)
- Minimum deviation, \( D_m = 36^\circ \)

2. **Calculate \( \frac{A + D_m}{2} \):**
\[ A + D_m = 40^\circ + 36^\circ = 76^\circ \]
\[ \frac{A + D_m}{2} = \frac{76^\circ}{2} = 38^\circ \]

3. **Calculate \( \frac{A}{2} \):**
\[ \frac{A}{2} = \frac{40^\circ}{2} = 20^\circ \]

4. **Substitute these values into the refractive index formula:**
\[ \mu = \frac{\sin(38^\circ)}{\sin(20^\circ)} \]

5. **Calculate \( \sin(38^\circ) \) and \( \sin(20^\circ) \):**
- Using a calculator:
- \( \sin(38^\circ) \approx 0.6157 \)
- \( \sin(20^\circ) \approx 0.3420 \)

6. **Calculate the refractive index \( \mu \):**
\[ \mu = \frac{0.6157}{0.3420} \approx 1.80 \]

### Final Answer:
The refractive index of the glass is approximately \( \mu \approx 1.80 \).