How much water should be filled in a container of height `21 cm,` so that it appears half filled to the observer when viewed from the top of the container `(mu=4//3).`

Options

A. 8 cm
B. 10.5 cm
C. 12 cm
D. 14 cm

Explanation

To solve the problem of how much water should be filled in a container of height 21 cm so that it appears half-filled to an observer when viewed from the top, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have a container with a total height of 21 cm.
- We need to find the height of water (let's denote it as \( X \)) such that when viewed from the top, it appears half-filled.

2. **Using the Concept of Apparent Height**:
- The refractive index of water (\( \mu \)) is given as \( \frac{4}{3} \).
- When viewed from the top, the apparent height of the water column is given by the formula:
\[ \text{Apparent Height} = \frac{X}{\mu} \]
- Since the observer sees the container as half-filled, the apparent height should equal half of the total height of the container:
\[ \frac{X}{\mu} = \frac{21}{2} \]

3. **Setting Up the Equation**:
- We can express the equation as:
\[ \frac{X}{\frac{4}{3}} = \frac{21}{2} \]
- To eliminate the fraction, we can multiply both sides by \( \frac{4}{3} \):
\[ X = \frac{21}{2} \times \frac{4}{3} \]

4. **Calculating the Value of \( X \)**:
- Now, simplifying the right side:
\[ X = \frac{21 \times 4}{2 \times 3} = \frac{84}{6} = 14 \text{ cm} \]

5. **Conclusion**:
- Therefore, the height of water that should be filled in the container is \( 14 \) cm.

### Final Answer:
The height of water that should be filled in the container is **14 cm**.