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 vertical pole as seen by a fish just below the water surface. The actual height of the pole is given as 24 cm, and the refractive index of water is given as \( \mu = \frac{4}{3} \).

### Step-by-Step Solution:

1. **Understanding 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 less than its actual height due to the refraction of light. The relationship between the apparent height (h') and the actual height (h) can be expressed using the refractive index (μ):
\[ \frac{h'}{h} = \frac{1}{\mu} \]

2. **Substituting the Known Values**:
Here, the actual height \( h = 24 \) cm, and the refractive index \( \mu = \frac{4}{3} \). We can substitute these values into the equation:
\[ \frac{h'}{24} = \frac{1}{\frac{4}{3}} \]

3. **Calculating the Apparent Height**:
Rearranging the equation to find \( h' \):
\[ h' = 24 \times \frac{1}{\frac{4}{3}} = 24 \times \frac{3}{4} \]
Simplifying this gives:
\[ h' = 24 \times 0.75 = 18 \text{ cm} \]

4. **Conclusion**:
Therefore, the apparent height of the tip of the pole as seen by the fish just below the water surface is **18 cm**.

### Final Answer:
The tip of the pole appears to be **18 cm** above the water surface to the underwater fish.