If the speed of light in diamond is `1.24xx10^8` m/s, find its refractive index.

Answer

To find the refractive index of diamond given the speed of light in diamond, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Speed of light in diamond (v_d) = \(1.24 \times 10^8\) m/s
- Speed of light in air (v_a) = \(3.00 \times 10^8\) m/s

2. **Understand the Formula for Refractive Index**:
- The refractive index (n) of a medium is given by the formula:
\[ n = \frac{v_a}{v_d} \]
where \(v_a\) is the speed of light in air and \(v_d\) is the speed of light in the medium (diamond in this case).

3. **Substitute the Values into the Formula**:
- Plugging in the values we have:
\[ n = \frac{3.00 \times 10^8 \text{ m/s}}{1.24 \times 10^8 \text{ m/s}} \]

4. **Perform the Division**:
- Calculate the division:
\[ n = \frac{3.00}{1.24} \approx 2.41935 \]

5. **Round the Result**:
- Rounding to two decimal places, we get:
\[ n \approx 2.42 \]

### Final Answer:
The refractive index of diamond is approximately **2.42**.

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