The refractive index of water with respect to air is `""_(a)mu_(w)` and of glass with respect to air is `""_(a)mu_(g)`. Express the refractive index of glass with respect to water.

Answer

To find the refractive index of glass with respect to water, we can use the given refractive indices of water and glass with respect to air. Here’s the step-by-step solution:

### Step 1: Write the refractive index of water with respect to air.
The refractive index of water with respect to air is given as:
\[ \mu_{w} = \frac{n_{w}}{n_{a}} \]
where \( n_{w} \) is the refractive index of water and \( n_{a} \) is the refractive index of air.

### Step 2: Write the refractive index of glass with respect to air.
The refractive index of glass with respect to air is given as:
\[ \mu_{g} = \frac{n_{g}}{n_{a}} \]
where \( n_{g} \) is the refractive index of glass.

### Step 3: Set up the equations.
From the above definitions, we can express these as:
1. \(\mu_{w} = \frac{n_{w}}{n_{a}}\) (Equation 1)
2. \(\mu_{g} = \frac{n_{g}}{n_{a}}\) (Equation 2)

### Step 4: Divide the refractive index of glass by that of water.
To find the refractive index of glass with respect to water, we can divide Equation 2 by Equation 1:
\[ \frac{\mu_{g}}{\mu_{w}} = \frac{\frac{n_{g}}{n_{a}}}{\frac{n_{w}}{n_{a}}} \]

### Step 5: Simplify the equation.
This simplifies to:
\[ \frac{\mu_{g}}{\mu_{w}} = \frac{n_{g}}{n_{w}} \]
Thus, the refractive index of glass with respect to water is:
\[ \mu_{g/w} = \frac{n_{g}}{n_{w}} = \frac{\mu_{g}}{\mu_{w}} \]

### Final Answer:
The refractive index of glass with respect to water is:
\[ \mu_{g/w} = \frac{\mu_{g}}{\mu_{w}} \]

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