The refractive indices of glass and water are `3/2` and `4/3` respectively. The refractive index of glass with respect to water is

Options

A. 2
B. `8/9`
C. `9/8`
D. `5/3`

Explanation

To find the refractive index of glass with respect to water, we can use the formula:

\[ \mu_{glass/water} = \frac{\mu_{glass}}{\mu_{water}} \]

Where:
- \(\mu_{glass}\) is the refractive index of glass with respect to air.
- \(\mu_{water}\) is the refractive index of water with respect to air.

Given:
- \(\mu_{glass} = \frac{3}{2}\)
- \(\mu_{water} = \frac{4}{3}\)

### Step 1: Write the formula for refractive index of glass with respect to water.

\[ \mu_{glass/water} = \frac{\mu_{glass}}{\mu_{water}} \]

### Step 2: Substitute the values of \(\mu_{glass}\) and \(\mu_{water}\).

\[ \mu_{glass/water} = \frac{\frac{3}{2}}{\frac{4}{3}} \]

### Step 3: Simplify the expression.

To simplify \(\frac{\frac{3}{2}}{\frac{4}{3}}\), we can multiply by the reciprocal of the denominator:

\[ \mu_{glass/water} = \frac{3}{2} \times \frac{3}{4} \]

### Step 4: Perform the multiplication.

\[ \mu_{glass/water} = \frac{3 \times 3}{2 \times 4} = \frac{9}{8} \]

### Final Answer:

The refractive index of glass with respect to water is \(\frac{9}{8}\).

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