If the speed of light in air is `3 xx 10^8` m/s, and the refractive index of water is 1.33, find the speed of light in water.

Answer

To find the speed of light in water, we can use the relationship between the speed of light in air, the refractive index, and the speed of light in water. Here’s the step-by-step solution:

### Step 1: Understand the formula for refractive index
The refractive index (n) of a medium is defined as the ratio of the speed of light in a vacuum (or air) to the speed of light in that medium. The formula is given by:
\[ n = \frac{c}{v} \]
where:
- \( n \) is the refractive index,
- \( c \) is the speed of light in air (or vacuum),
- \( v \) is the speed of light in the medium (in this case, water).

### Step 2: Rearrange the formula to find the speed of light in water
From the formula, we can rearrange it to find the speed of light in water:
\[ v = \frac{c}{n} \]

### Step 3: Substitute the known values
We know:
- The speed of light in air, \( c = 3 \times 10^8 \) m/s,
- The refractive index of water, \( n = 1.33 \).

Now substitute these values into the rearranged formula:
\[ v = \frac{3 \times 10^8 \text{ m/s}}{1.33} \]

### Step 4: Perform the calculation
Now, we will calculate the speed of light in water:
\[ v \approx \frac{3 \times 10^8}{1.33} \]
\[ v \approx 2.256 \times 10^8 \text{ m/s} \]

### Step 5: Round the answer
Rounding to two decimal places, we get:
\[ v \approx 2.25 \times 10^8 \text{ m/s} \]

### Final Answer
The speed of light in water is approximately \( 2.25 \times 10^8 \) m/s.

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