Calculate the refractive index of the material of an equilaterial prism for which angle of minimum deviation is `60^@`.

Explanation

To calculate the refractive index of the material of an equilateral prism given that the angle of minimum deviation (δ) is 60 degrees, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Angle of the prism (A) = 60 degrees (since it is an equilateral prism).
- Angle of minimum deviation (δ) = 60 degrees.

2. **Use the Formula for Refractive Index**:
The formula for the refractive index (μ) of a prism in terms of the angle of the prism and the angle of minimum deviation is given by:
\[ \mu = \frac{A + \delta}{2 \sin(\frac{A}{2})} \]

3. **Substitute the Values into the Formula**:
- Substitute A = 60 degrees and δ = 60 degrees into the formula:
\[ \mu = \frac{60 + 60}{2 \sin(\frac{60}{2})} \]

4. **Calculate the Values**:
- First, calculate \( A + \delta \):
\[ A + \delta = 60 + 60 = 120 \text{ degrees} \]
- Now, calculate \( \frac{A}{2} \):
\[ \frac{A}{2} = \frac{60}{2} = 30 \text{ degrees} \]
- Now, find \( \sin(30) \):
\[ \sin(30) = \frac{1}{2} \]

5. **Substitute Back into the Formula**:
\[ \mu = \frac{120}{2 \cdot \frac{1}{2}} = \frac{120}{1} = 120 \]

6. **Final Calculation**:
- The refractive index is:
\[ \mu = 2 \sqrt{3} \approx 3.464 \]

### Final Answer:
The refractive index of the material of the equilateral prism is \( \sqrt{3} \).