How does the refractive index of a medium depend on its temperature ?

Answer

### Step-by-Step Solution:

1. **Understanding Refractive Index**:
The refractive index (n) of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in the medium (v). Mathematically, it is expressed as:
\[ n = \frac{c}{v} \]

2. **Effect of Temperature on Medium**:
As the temperature of a medium increases, the kinetic energy of its particles also increases. This results in a change in the properties of the medium.

3. **Velocity of Light in the Medium**:
With an increase in temperature, the velocity (v) of light in the medium increases. This is because the increased energy causes the particles in the medium to vibrate more rapidly, allowing light to pass through more quickly.

4. **Relationship Between Speed and Refractive Index**:
Since the refractive index is inversely proportional to the speed of light in the medium, an increase in velocity (v) leads to a decrease in the refractive index (n):
\[ n \propto \frac{1}{v} \]

5. **Conclusion**:
Therefore, as the temperature of the medium increases, the refractive index decreases. This inverse relationship indicates that higher temperatures result in lower refractive indices.