To calculate the speed of light in water using its refractive index, you divide the speed of light in a vacuum by the refractive index of water.
The relationship between the speed of light in a vacuum, the speed of light in a medium, and the refractive index of that medium is fundamental in optics. The refractive index ($n$) of a medium is defined as the ratio of the speed of light in a vacuum ($c$) to the speed of light in that medium ($v$).
Mathematically, this relationship is expressed as:
$n = \frac{c}{v}$
To find the speed of light in the medium ($v$), you can rearrange the formula:
$v = \frac{c}{n}$
Applying the Formula for Water
Based on the provided information:
- The speed of light in a vacuum (or air) is approximately $3 \times 10^8$ meters per second (m/s). This value is represented by 'c'.
- The refractive index of water is given as 1.3. This value is represented by 'n'.
Using the formula $v = \frac{c}{n}$, we can calculate the speed of light in water ($v_{\text{water}}$):
$v_{\text{water}} = \frac{\text{Speed of light in vacuum}}{\text{Refractive index of water}}$
$v_{\text{water}} = \frac{3 \times 10^8 \text{ m/s}}{1.3}$
The Calculation and Result
Performing the division:
$v_{\text{water}} \approx 2.3 \times 10^8 \text{ m/s}$
Therefore, the velocity of light in water is approximately $2.3 \times 10^8$ m/s.
Summary of Calculation
Here is a summary of the calculation:
| Parameter | Symbol | Value | Unit |
|---|---|---|---|
| Speed of light in vacuum | c | $3 \times 10^8$ | m/s |
| Refractive index of water | n | 1.3 | - |
| Speed of light in water | v | $(3 \times 10^8) / 1.3$ | m/s |
| Calculated Speed | v | $2.3 \times 10^8$ | m/s |
This method is widely used to determine how light slows down when passing through different transparent materials. The higher the refractive index of a material, the slower light travels through it.
