`µ_(1)` and `µ_(2)` are the refractive index of two mediums and `v_(1)` and `v_(2)` are the velocity of light in these in two mediums respectively. Then, the relation connecting these quantities is

Options

A. `v_(1)=v_(2)`
B. `µ_(2)v_(1)= µ_(1)v_(2)`
C. `µ_(1)^(2)v_(1)= µ_(2)^(2)v_(2)`
D. `µ_(1)v_(1)= µ_(2)v_(2)`

Explanation

To find the relation connecting the refractive indices \( \mu_1 \) and \( \mu_2 \) of two mediums and the velocities of light \( v_1 \) and \( v_2 \) in those mediums, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Refractive Index**:
The refractive index \( \mu \) 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, this is expressed as:
\[ \mu = \frac{c}{v} \]

2. **Applying the Definition for Medium 1**:
For the first medium, we denote the refractive index as \( \mu_1 \) and the speed of light in this medium as \( v_1 \). According to the definition:
\[ \mu_1 = \frac{c}{v_1} \]
Rearranging this gives:
\[ c = \mu_1 v_1 \quad \text{(Equation 1)} \]

3. **Applying the Definition for Medium 2**:
Similarly, for the second medium, we denote the refractive index as \( \mu_2 \) and the speed of light in this medium as \( v_2 \):
\[ \mu_2 = \frac{c}{v_2} \]
Rearranging this gives:
\[ c = \mu_2 v_2 \quad \text{(Equation 2)} \]

4. **Equating the Two Expressions for \( c \)**:
Since both expressions equal \( c \), we can set them equal to each other:
\[ \mu_1 v_1 = \mu_2 v_2 \]

5. **Final Relation**:
Thus, the relation connecting the refractive indices and the velocities of light in the two mediums is:
\[ \mu_1 v_1 = \mu_2 v_2 \]

### Conclusion:
The final answer is:
\[ \mu_1 v_1 = \mu_2 v_2 \]