The speed of light in diamond is `125,000" km "s^(-1)` what is its refractive index ? (Speed of light in air `=3xx10^(8)ms^(-1)`).

Answer

To find the refractive index of diamond, we can follow these steps:

### Step 1: Convert the speed of light in diamond from kilometers per second to meters per second.
Given:
- Speed of light in diamond = 125,000 km/s

To convert kilometers to meters, we multiply by 1000:
\[ 125,000 \, \text{km/s} = 125,000 \times 1000 \, \text{m/s} = 125,000,000 \, \text{m/s} = 1.25 \times 10^8 \, \text{m/s} \]

### Step 2: Write down the speed of light in air.
Given:
- Speed of light in air = \(3 \times 10^8 \, \text{m/s}\)

### Step 3: Use the formula for refractive index.
The refractive index \( n \) is given by the formula:
\[ n = \frac{\text{Speed of light in air}}{\text{Speed of light in diamond}} \]

### Step 4: Substitute the values into the formula.
Substituting the known values:
\[ n = \frac{3 \times 10^8 \, \text{m/s}}{1.25 \times 10^8 \, \text{m/s}} \]

### Step 5: Simplify the expression.
Calculating the refractive index:
\[ n = \frac{3}{1.25} = 2.4 \]

### Step 6: Final answer.
Thus, the refractive index of diamond is:
\[ n \approx 2.4 \]