The refractive index of water is `(4//3)` and that of glass is `(3//2)` . If the speed of light in glass is `2xx 10^(8) m//s` . The speed of light in water will be:

Options

A. `1 xx 10^(8) m//s`
B. `(9//4) xx 10^(8) m//s`
C. ` (8//3) xx 10^(8) m//s`
D. `4 xx 10^(8) m//s`

Answer

To find the speed of light in water given the refractive indices and the speed of light in glass, we can follow these steps:

### Step 1: Understand the relationship between refractive index and speed of light
The refractive index (µ) of a medium is defined as the ratio of the speed of light in vacuum (or air) (c) to the speed of light in that medium (v). Mathematically, this can be expressed as:
\[ \mu = \frac{c}{v} \]
For two different media, we can write:
\[ \frac{\mu_{water}}{\mu_{glass}} = \frac{v_{glass}}{v_{water}} \]

### Step 2: Substitute the known values
Given:
- Refractive index of water, \( \mu_{water} = \frac{4}{3} \)
- Refractive index of glass, \( \mu_{glass} = \frac{3}{2} \)
- Speed of light in glass, \( v_{glass} = 2 \times 10^8 \, m/s \)

Substituting these values into the equation:
\[ \frac{\frac{4}{3}}{\frac{3}{2}} = \frac{2 \times 10^8}{v_{water}} \]

### Step 3: Simplify the left side of the equation
To simplify \( \frac{\frac{4}{3}}{\frac{3}{2}} \):
\[ \frac{4}{3} \times \frac{2}{3} = \frac{8}{9} \]
So, the equation becomes:
\[ \frac{8}{9} = \frac{2 \times 10^8}{v_{water}} \]

### Step 4: Rearrange to solve for \( v_{water} \)
Cross-multiplying gives:
\[ 8 \cdot v_{water} = 9 \cdot (2 \times 10^8) \]
\[ v_{water} = \frac{9 \cdot (2 \times 10^8)}{8} \]

### Step 5: Calculate \( v_{water} \)
Calculating the right side:
\[ v_{water} = \frac{18 \times 10^8}{8} = \frac{9 \times 10^8}{4} \]
\[ v_{water} = 2.25 \times 10^8 \, m/s \]

### Final Answer
The speed of light in water is:
\[ v_{water} = 2.25 \times 10^8 \, m/s \]

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