The refractive index of water is 1.33. What will be the speed of light in water

Options

A. `4xx10^(8)m//s`
B. `1.33xx10^(8)m//s`
C. `3xx10^(8)m//s`
D. `2.25xx10^(8)m//s`

Answer

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

### Step-by-Step Solution:

1. **Understand the Definition of Refractive Index:**
The refractive index (μ) of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in that medium (v). Mathematically, this is expressed as:
\[ \mu = \frac{c}{v} \]

2. **Identify the Given Values:**
- The refractive index of water (μ) is given as 1.33.
- The speed of light in vacuum (c) is approximately \(3 \times 10^8\) meters per second.

3. **Rearrange the Formula to Find Speed in the Medium:**
From the definition of refractive index, we can rearrange the formula to solve for the speed of light in water (v):
\[ v = \frac{c}{\mu} \]

4. **Substitute the Known Values:**
Now, substitute the known values into the rearranged formula:
\[ v = \frac{3 \times 10^8 \text{ m/s}}{1.33} \]

5. **Calculate the Speed of Light in Water:**
Performing the calculation:
\[ v \approx \frac{3 \times 10^8}{1.33} \approx 2.26 \times 10^8 \text{ m/s} \]

6. **Final Result:**
Thus, the speed of light in water is approximately:
\[ v \approx 2.26 \times 10^8 \text{ m/s} \]