11.If the index of refraction for water 1.33 and the speed of light in vacuum is 3 × 108 m/s.ABCD

To solve the problem, we need to determine the speed of light in water using the index of refraction. Here’s how to approach this:

1. Break Down the Problem

We need to find the speed of light in water using the formula that relates the index of refraction (n), the speed of light in vacuum (c), and the speed of light in a medium (v).

2. Relevant Concepts

The formula that relates these quantities is: $n = \frac{c}{v}$ Where:

• $n$ = index of refraction
• $c$ = speed of light in vacuum
• $v$ = speed of light in the medium (water in this case)

3. Analysis and Detail

Given:

• $n = 1.33$ (index of refraction for water)
• $c = 3 \times 10^8 \, \text{m/s}$

We rearrange the equation to solve for $v$: $v = \frac{c}{n}$

Now, substitute the values: $v = \frac{3 \times 10^8 \, \text{m/s}}{1.33}$

Calculating $v$: $v \approx 2.26 \times 10^8 \, \text{m/s}$

4. Verify and Summarize

The speed of light in water was calculated as approximately $2.26 \times 10^8 \, \text{m/s}$. This value is lower than the speed of light in vacuum, which is expected due to the refractive properties of water.

Final Answer

The speed of light in water is approximately $2.26 \times 10^8 \, \text{m/s}$.