The refractive index of water with respect to air is `4//3`. What is the refractive index of aiir with respect to water ?

Answer

To find the refractive index of air with respect to water when the refractive index of water with respect to air is given as \( \frac{4}{3} \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
The refractive index of water with respect to air is given as \( n_{wa} = \frac{4}{3} \).

2. **Use the Formula for Refractive Index**:
The refractive index of a medium A with respect to medium B is defined as:
\[ n_{AB} = \frac{c}{v} \]
where \( c \) is the speed of light in vacuum, and \( v \) is the speed of light in the medium.

3. **Reciprocal Relationship**:
The refractive index of air with respect to water can be found using the reciprocal of the refractive index of water with respect to air:
\[ n_{aw} = \frac{1}{n_{wa}} \]

4. **Substitute the Given Value**:
Now, substitute the value of \( n_{wa} \):
\[ n_{aw} = \frac{1}{\frac{4}{3}} \]

5. **Simplify the Expression**:
To simplify \( \frac{1}{\frac{4}{3}} \), we can multiply by the reciprocal:
\[ n_{aw} = \frac{3}{4} \]

6. **Final Answer**:
Therefore, the refractive index of air with respect to water is:
\[ n_{aw} = \frac{3}{4} \]

### Final Answer:
The refractive index of air with respect to water is \( \frac{3}{4} \).