Suppose the medium in the previous question is water. Select the correct option s from the list given in that question.

Answer

To solve the problem, we need to analyze the situation involving three observers (A, B, and C) measuring the speed of light in water. Let's break down the steps to find the relationship between their measured speeds.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- Observer A is moving towards the light source.
- Observer B is stationary.
- Observer C is moving away from the light source.
- The medium is water.

2. **Speed of Light in Different Mediums**:
- The speed of light in a vacuum is constant, but in a medium like water, it is affected by the motion of the observer relative to the medium.
- The speed of light in water is less than in vacuum, but the perceived speed will change based on the observer's motion.

3. **Analyzing Observer A**:
- Since observer A is moving towards the source, the speed of light measured by A (VA) will be greater than the speed measured by B (VB), who is stationary. Thus, we can write:
\[ VA > VB \]

4. **Analyzing Observer C**:
- Observer C is moving away from the source. Therefore, the speed of light measured by C (VC) will be less than the speed measured by B (VB). Thus, we can write:
\[ VB > VC \]

5. **Combining the Relationships**:
- From the above two inequalities, we can combine them to get:
\[ VA > VB > VC \]

6. **Equal Magnitudes of VA and VC**:
- The problem states that the magnitudes of the speeds of A and C are equal but in opposite directions. This means:
\[ |VA| = |VC| \]
- Since they are in opposite directions, this does not affect the inequality derived earlier.

7. **Finding the Average Speed**:
- We can express the relationship mathematically. Since VA and VC are equal in magnitude:
\[ VB = \frac{VA + VC}{2} \]
- This shows that the speed of B is the average of the speeds of A and C.

### Conclusion:
From the analysis, we conclude that:
- The correct relationship is:
\[ VA > VB > VC \]
- Additionally, we have:
\[ VB = \frac{VA + VC}{2} \]

### Final Answer:
- The correct options are:
- Option A: \( VA > VB > VC \)
- Option B: \( VB = \frac{1}{2}(VA + VC) \)