Velocity (v) of light in a medium (refractive index `mu`) vary as

Options

A. `mupropv^(2)`
B. `muprop1/v^(2)`
C. `mupropv`
D. `muprop1/v`

Answer

To determine how the velocity of light in a medium varies with its refractive index, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Refractive Index**:
The refractive index (μ) 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).
\[ \mu = \frac{C}{V} \]

2. **Expressing the Relationship**:
Rearranging the formula gives us:
\[ V = \frac{C}{\mu} \]
This shows that the speed of light in a medium (V) is equal to the speed of light in vacuum (C) divided by the refractive index (μ).

3. **Identifying Constants**:
The speed of light in vacuum (C) is a constant value, approximately \(3 \times 10^8\) meters per second.

4. **Analyzing the Variation**:
From the equation \(V = \frac{C}{\mu}\), we can see that as the refractive index (μ) increases, the speed of light in the medium (V) decreases. This indicates that the velocity of light in a medium is inversely proportional to the refractive index.
\[ V \propto \frac{1}{\mu} \]

5. **Conclusion**:
Therefore, the velocity of light in a medium varies inversely with the refractive index of that medium.

### Final Answer:
The velocity of light in a medium (V) is inversely proportional to the refractive index (μ):
\[ V \propto \frac{1}{\mu} \]