If the refractive index of ice is 1.31, what will be the speed of light in it?

Answer

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

### Step-by-Step Solution:

1. **Identify the known values**:
- Refractive index of ice (n) = 1.31
- Speed of light in air (c) = \(3 \times 10^8\) meters per second.

2. **Use the formula for refractive index**:
The refractive index (n) is defined as the ratio of the speed of light in a vacuum (or air) to the speed of light in the medium (ice in this case). This can be expressed as:
\[ n = \frac{c}{v} \]
where:
- \(c\) = speed of light in air (or vacuum)
- \(v\) = speed of light in the medium (ice).

3. **Rearrange the formula to find the speed of light in ice**:
To find the speed of light in ice (v), we can rearrange the formula:
\[ v = \frac{c}{n} \]

4. **Substitute the known values into the equation**:
Now, substitute the known values into the equation:
\[ v = \frac{3 \times 10^8 \text{ m/s}}{1.31} \]

5. **Calculate the speed of light in ice**:
Performing the division:
\[ v \approx \frac{3 \times 10^8}{1.31} \approx 2.29 \times 10^8 \text{ m/s} \]

6. **Conclusion**:
The speed of light in ice is approximately \(2.29 \times 10^8\) meters per second.