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

Options

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

Answer

To find the speed of light in water given its refractive index, we can use the formula for refractive index (μ):

\[ \mu = \frac{c}{v} \]

Where:
- \( \mu \) is the refractive index,
- \( c \) is the speed of light in a vacuum (approximately \( 3 \times 10^8 \) m/s),
- \( v \) is the speed of light in the medium (in this case, water).

### Step-by-Step Solution:

1. **Identify the given values:**
- Refractive index of water, \( \mu = 1.33 \)
- Speed of light in vacuum, \( c = 3 \times 10^8 \) m/s

2. **Rearrange the formula to solve for \( v \):**
\[ v = \frac{c}{\mu} \]

3. **Substitute the known values into the equation:**
\[ v = \frac{3 \times 10^8 \text{ m/s}}{1.33} \]

4. **Perform the division:**
- First, calculate \( \frac{3}{1.33} \):
\[ \frac{3}{1.33} \approx 2.2565 \]
- Now, multiply by \( 10^8 \):
\[ v \approx 2.2565 \times 10^8 \text{ m/s} \]

5. **Round to an appropriate number of significant figures:**
- Rounding \( 2.2565 \) gives approximately \( 2.25 \).
- Thus, the speed of light in water is:
\[ v \approx 2.25 \times 10^8 \text{ m/s} \]

### Final Answer:
The speed of light in water is approximately \( 2.25 \times 10^8 \) meters per second.

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