An under water swimmer is at a depth of 12 m below the surface of water. A bird is at a height of 18 m from the surface of water, directly above his eyes. For the swimmer the bird appears to be at a distance from the surface of water equal to (Refractive Index of water is 4/3)

Options

A. 24 m
B. 12 m
C. 18 m
D. 9 m

Explanation

To solve the problem, we need to find the apparent height of the bird as seen by the underwater swimmer. We will use the concept of refraction and the formula for apparent depth.

### Step-by-Step Solution:

1. **Identify the given values:**
- Depth of the swimmer (h₁) = 12 m (below the surface of the water)
- Height of the bird (h₂) = 18 m (above the surface of the water)
- Refractive index of water (μ) = 4/3

2. **Calculate the total distance from the swimmer to the bird:**
- The total distance from the swimmer to the bird is the sum of the depth of the swimmer and the height of the bird.
\[ \text{Total distance} = h₁ + h₂ = 12 \, \text{m} + 18 \, \text{m} = 30 \, \text{m} \]

3. **Use the formula for apparent height:**
- The apparent height (h') of the bird as seen by the swimmer can be calculated using the formula:
\[ h' = \frac{h}{\mu} \]
where \( h \) is the actual height of the bird above the water surface, and \( \mu \) is the refractive index of water.

4. **Substituting the values:**
- Here, the actual height (h) is 18 m (the height of the bird above the water surface).
\[ h' = \frac{18 \, \text{m}}{\frac{4}{3}} = 18 \, \text{m} \times \frac{3}{4} = 13.5 \, \text{m} \]

5. **Calculate the apparent distance from the surface of the water:**
- Since the swimmer is at a depth of 12 m, the apparent distance of the bird from the surface of the water is:
\[ \text{Apparent distance from surface} = h' + h₁ = 13.5 \, \text{m} + 12 \, \text{m} = 25.5 \, \text{m} \]

### Final Answer:
The bird appears to be at a distance of **25.5 m** from the surface of the water for the swimmer.