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 of the container, we can follow these steps:

### Step-by-Step Solution:

1. **Define Variables**:
- Let the height of water in the container be \( H \).
- The total height of the container is given as \( 21 \) cm.

2. **Determine the Apparent Height**:
- The apparent height of the water when viewed from the top is given by the formula:
\[ \text{Apparent Height} = \frac{H}{\mu} \]
- Here, \( \mu \) (the refractive index of water) is given as \( \frac{4}{3} \).

3. **Set the Condition for Half-Filled**:
- For the container to appear half-filled, the apparent height of the water should equal half of the total height of the container:
\[ \text{Apparent Height} = \frac{21}{2} = 10.5 \text{ cm} \]

4. **Set Up the Equation**:
- From the previous steps, we can set up the equation:
\[ \frac{H}{\frac{4}{3}} = 10.5 \]
- This simplifies to:
\[ H = 10.5 \times \frac{4}{3} \]

5. **Calculate \( H \)**:
- Now, calculate \( H \):
\[ H = 10.5 \times \frac{4}{3} = 10.5 \times 1.3333 \approx 14 \text{ cm} \]

6. **Determine the Height of Water**:
- Since the total height of the container is \( 21 \) cm, the height of water that should be filled is:
\[ H = 14 \text{ cm} \]

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

---