Find the velocity of light in water, if its velocity in glass of refractive index 1.5 is `2 xx 10^(8)m//s`. The refractive index of water is 1.33.

Options

A. `1.25 xx 10^(8)m//s`
B. `2.20 xx 10^(8) m//s`
C. `2.15 xx 10^(8)m//s`
D. `2.25 xx 10^(8) m//s`

Explanation

To find the velocity of light in water, we can use the relationship between the velocity of light in different mediums and their refractive indices. Here’s a step-by-step solution:

### Step 1: Understand the relationship between velocity and refractive index
The refractive index (n) 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):
\[ n = \frac{c}{v} \]

### Step 2: Find the velocity of light in air
The speed of light in air is approximately the same as in vacuum, which is:
\[ c \approx 3 \times 10^8 \, \text{m/s} \]

### Step 3: Use the refractive index of glass to find the speed of light in air
Given that the refractive index of glass (n_glass) is 1.5 and the speed of light in glass (v_glass) is \( 2 \times 10^8 \, \text{m/s} \), we can rearrange the formula to find the speed of light in air:
\[ n_{glass} = \frac{c}{v_{glass}} \]
\[ 1.5 = \frac{3 \times 10^8}{2 \times 10^8} \]

### Step 4: Use the refractive index of water to find the speed of light in water
The refractive index of water (n_water) is given as 1.33. We can use the same formula to find the speed of light in water (v_water):
\[ n_{water} = \frac{c}{v_{water}} \]
Rearranging gives:
\[ v_{water} = \frac{c}{n_{water}} \]

### Step 5: Substitute the values
Substituting the known values:
\[ v_{water} = \frac{3 \times 10^8}{1.33} \]

### Step 6: Calculate the value
Now, we calculate:
\[ v_{water} = \frac{3 \times 10^8}{1.33} \approx 2.26 \times 10^8 \, \text{m/s} \]

### Final Answer
The velocity of light in water is approximately:
\[ v_{water} \approx 2.26 \times 10^8 \, \text{m/s} \]

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