`""_(i)u_(j)` represents refractive index when a light ray goes from medium `i` to medium `j`, then the product `""_(2)µ_(1)xx``""_(3)µ_(2)xx``""_(4)µ_(2)` is equal to

Options

A. `""_(3)µ_(1)`
B. `""_(3)µ_(2)`
C. `(1)/(""_(1)µ_(4))`
D. `""_(4)µ_(2)`

Explanation

To solve the problem, we need to analyze the expression given in the question, which involves the refractive indices between different media.

### Step-by-Step Solution:

1. **Understand the Notation**:
- The notation \( \mu_{i j} \) represents the refractive index when light travels from medium \( i \) to medium \( j \). This can be expressed as:
\[ \mu_{i j} = \frac{\mu_j}{\mu_i} \]
- Here, \( \mu_j \) is the refractive index of medium \( j \) and \( \mu_i \) is the refractive index of medium \( i \).

2. **Write the Given Product**:
- We need to evaluate the product:
\[ 2 \mu_1 \cdot 3 \mu_2 \cdot 4 \mu_3 \]

3. **Express Each Term Using the Refractive Index Definition**:
- Using the definition of refractive indices, we can express each term as follows:
\[ \mu_{2 1} = \frac{\mu_1}{\mu_2}, \quad \mu_{3 2} = \frac{\mu_2}{\mu_3}, \quad \mu_{4 3} = \frac{\mu_3}{\mu_4} \]

4. **Combine the Products**:
- Now, we can rewrite the product:
\[ 2 \mu_1 \cdot 3 \mu_2 \cdot 4 \mu_3 = 2 \cdot 3 \cdot 4 \cdot \mu_1 \cdot \mu_2 \cdot \mu_3 \]

5. **Substituting the Refractive Indices**:
- We can express the product of refractive indices in terms of each other:
\[ \mu_{2 1} \cdot \mu_{3 2} \cdot \mu_{4 3} = \left(\frac{\mu_1}{\mu_2}\right) \cdot \left(\frac{\mu_2}{\mu_3}\right) \cdot \left(\frac{\mu_3}{\mu_4}\right) \]

6. **Cancel Out Terms**:
- Notice that \( \mu_2 \) and \( \mu_3 \) cancel out:
\[ \mu_{2 1} \cdot \mu_{3 2} \cdot \mu_{4 3} = \frac{\mu_1}{\mu_4} \]

7. **Final Expression**:
- Therefore, the product simplifies to:
\[ \frac{\mu_1}{\mu_4} \]

8. **Conclusion**:
- The final answer is \( \mu_{1 4} \), which represents the refractive index when light travels from medium 1 to medium 4.

### Final Answer:
\[ \mu_{1 4} \]