Absolute refractive indices of glass and water are `3//2` and `4//3`. The ratio of velocity of light in glass and water will be

Options

A. `4 : 3`
B. `9 : 8`
C. `8 : 9`
D. `3 : 4`

Explanation

To find the ratio of the velocity of light in glass and water given their absolute refractive indices, we can follow these steps:

### Step 1: Understand the relationship between refractive index and velocity of light
The refractive index (μ) 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). This can be expressed as:
\[ \mu = \frac{C}{V} \]
From this, we can rearrange the formula to find the velocity of light in the medium:
\[ V = \frac{C}{\mu} \]

### Step 2: Write the expression for the ratio of velocities
We need to find the ratio of the velocity of light in glass (V_g) to the velocity of light in water (V_w):
\[ \frac{V_g}{V_w} = \frac{C/\mu_g}{C/\mu_w} \]
Here, μ_g is the refractive index of glass, and μ_w is the refractive index of water.

### Step 3: Simplify the expression
Since C (the speed of light in vacuum) is a common factor in both the numerator and the denominator, it cancels out:
\[ \frac{V_g}{V_w} = \frac{\mu_w}{\mu_g} \]

### Step 4: Substitute the given refractive indices
From the problem, we know:
- Refractive index of glass (μ_g) = \( \frac{3}{2} \)
- Refractive index of water (μ_w) = \( \frac{4}{3} \)

Substituting these values into the ratio:
\[ \frac{V_g}{V_w} = \frac{\frac{4}{3}}{\frac{3}{2}} \]

### Step 5: Simplify the fraction
To simplify the fraction, we multiply by the reciprocal of the denominator:
\[ \frac{V_g}{V_w} = \frac{4}{3} \times \frac{2}{3} = \frac{8}{9} \]

### Conclusion
Thus, the ratio of the velocity of light in glass to the velocity of light in water is:
\[ \frac{V_g}{V_w} = \frac{8}{9} \]

### Final Answer
The ratio of the velocity of light in glass and water is \( \frac{8}{9} \).

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