`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 solve the problem, we need to establish the relationship between the refractive indices and the velocities of light in two different media. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the definition of 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). Mathematically, this can be expressed as:
\[ µ = \frac{c}{v} \]

### Step 2: Express the speed of light in terms of refractive index
From the definition, we can rearrange the formula to express the speed of light in terms of the refractive index:
\[ v = \frac{c}{µ} \]

### Step 3: Apply the relationship to two different media
Let’s denote the refractive indices and velocities of light in two different media as follows:
- For medium 1:
- Refractive index = \( µ_1 \)
- Velocity of light = \( v_1 \)

- For medium 2:
- Refractive index = \( µ_2 \)
- Velocity of light = \( v_2 \)

Using the formula from Step 2 for both media, we can write:
\[ v_1 = \frac{c}{µ_1} \]
\[ v_2 = \frac{c}{µ_2} \]

### Step 4: Set up the relationship between the two media
Now, we can multiply the velocities by their respective refractive indices:
- For medium 1:
\[ v_1 \cdot µ_1 = c \]

- For medium 2:
\[ v_2 \cdot µ_2 = c \]

Since both expressions equal \( c \), we can set them equal to each other:
\[ v_1 \cdot µ_1 = v_2 \cdot µ_2 \]

### Step 5: Conclusion
Thus, the relationship connecting the refractive indices and the velocities of light in the two media is:
\[ v_1 \cdot µ_1 = v_2 \cdot µ_2 \]

### Final Answer
The correct relation is:
\[ v_1 \cdot µ_1 = v_2 \cdot µ_2 \]

---