The length of a vertical pole at the surface of a lake of water `(mu=4/3)` is 24 cm. Then to an under-water fish just below the water surface the tip of the pole appeard to be

Options

A. 18 cm above the surface
B. 24 cm above the surface
C. 32 cm above the surface
D. 36 cm above the surface

Answer

To solve the problem, we need to find the apparent height of the tip of a vertical pole when viewed by a fish just below the surface of the water. The given data includes:

- The actual length of the pole (real height) = 24 cm
- The refractive index of water (μ) = 4/3

### Step-by-Step Solution:

1. **Understand the Concept of Apparent Height**:
The apparent height of an object when viewed from a different medium (in this case, from water to air) is affected by the refractive index of the medium. The formula to relate the real height (h) and the apparent height (h') is given by:
\[ h' = \frac{h}{\mu} \]
where \( \mu \) is the refractive index of the medium.

2. **Identify the Given Values**:
- Real height (h) = 24 cm
- Refractive index (μ) = 4/3

3. **Calculate the Apparent Height**:
Using the formula:
\[ h' = \frac{h}{\mu} = \frac{24 \text{ cm}}{4/3} \]
To simplify this, we can multiply by the reciprocal of the refractive index:
\[ h' = 24 \text{ cm} \times \frac{3}{4} \]

4. **Perform the Calculation**:
\[ h' = 24 \times \frac{3}{4} = 24 \times 0.75 = 18 \text{ cm} \]

5. **Convert Apparent Height to Above Water Surface**:
Since the fish is just below the water surface, the apparent height of the tip of the pole above the water surface will be:
\[ \text{Height above water surface} = \text{Real height} + \text{Apparent height} \]
Therefore, the total height above the water surface is:
\[ \text{Total height} = 24 \text{ cm} + 18 \text{ cm} = 42 \text{ cm} \]

### Final Answer:
The tip of the pole appears to be 42 cm above the water surface to the fish just below the surface.

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