How does the refractive index of a medium depend on the wavelength of light used ?

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 that medium (v). Mathematically, it is expressed as:
\[ n = \frac{c}{v} \]

2. **Relationship with Wavelength**:
The speed of light in a medium is related to the wavelength (λ) of the light. According to the wave equation, the speed of light in a medium can be expressed as:
\[ v = f \cdot \lambda \]
where f is the frequency of the light wave.

3. **Frequency and Wavelength**:
The frequency of light remains constant when it passes from one medium to another. Therefore, if the wavelength changes, the speed of light in the medium will also change.

4. **Inversely Proportional Relationship**:
Since the refractive index is defined as the ratio of the speed of light in vacuum to the speed of light in the medium, we can see that:
\[ n = \frac{c}{f \cdot \lambda} \]
This indicates that if the wavelength (λ) increases, the speed of light in the medium (v) also increases, which in turn causes the refractive index (n) to decrease.

5. **Conclusion**:
Therefore, we conclude that the refractive index of a medium is inversely proportional to the wavelength of the light used. As the wavelength increases, the refractive index decreases, and vice versa.

### Summary Statement:
The refractive index of a medium is inversely proportional to the wavelength of light used; as the wavelength increases, the refractive index decreases.