The refractive index of water and glass with respect to air is 1.3 and 1.5 respectively, what will be the refractive index of glass with respect to water?

Options

A. `(1.5)/(1.3)`
B. `(1.3)/(1.5)`
C. `(1.5)/(2.6)`
D. `(2.6)/(1.5)`

Answer

To find the refractive index of glass with respect to water, we can use the relationship between the refractive indices of different media.

### Step-by-Step Solution:

1. **Identify the given refractive indices:**
- Refractive index of water with respect to air (μ_water/air) = 1.3
- Refractive index of glass with respect to air (μ_glass/air) = 1.5

2. **Use the formula for refractive indices:**
The refractive index of one medium with respect to another can be expressed as:
\[ \mu_{glass/water} = \frac{\mu_{glass/air}}{\mu_{water/air}} \]
where:
- μ_glass/water is the refractive index of glass with respect to water.
- μ_glass/air is the refractive index of glass with respect to air.
- μ_water/air is the refractive index of water with respect to air.

3. **Substitute the known values into the formula:**
\[ \mu_{glass/water} = \frac{1.5}{1.3} \]

4. **Calculate the refractive index:**
\[ \mu_{glass/water} = \frac{1.5}{1.3} \approx 1.1538 \]

5. **Final result:**
The refractive index of glass with respect to water is approximately 1.15.