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. `8:7`
C. `8:9`
D. `3:4`

Explanation

To find the ratio of the velocity of light in glass and water, we can use the relationship between the refractive index and the speed of light in different media. The refractive index (n) is defined as:

\[ n = \frac{c}{v} \]

where:
- \( c \) is the speed of light in vacuum,
- \( v \) is the speed of light in the medium.

Given:
- The absolute refractive index of glass, \( n_g = \frac{3}{2} \)
- The absolute refractive index of water, \( n_w = \frac{4}{3} \)

### Step 1: Write the formula for the speed of light in glass and water

From the definition of refractive index, we can express the speed of light in glass (\( v_g \)) and water (\( v_w \)) as:

\[ v_g = \frac{c}{n_g} \]
\[ v_w = \frac{c}{n_w} \]

### Step 2: Substitute the values of \( n_g \) and \( n_w \)

Substituting the values of the refractive indices:

\[ v_g = \frac{c}{\frac{3}{2}} = \frac{2c}{3} \]
\[ v_w = \frac{c}{\frac{4}{3}} = \frac{3c}{4} \]

### Step 3: Find the ratio of the velocities

Now, we can find the ratio of the velocities of light in glass and water:

\[ \frac{v_g}{v_w} = \frac{\frac{2c}{3}}{\frac{3c}{4}} \]

### Step 4: Simplify the ratio

To simplify the ratio:

\[ \frac{v_g}{v_w} = \frac{2c}{3} \times \frac{4}{3c} = \frac{2 \times 4}{3 \times 3} = \frac{8}{9} \]

### Conclusion

Thus, the ratio of the velocity of light in glass to the velocity of light in water is:

\[ \frac{v_g}{v_w} = \frac{8}{9} \]

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