A bird is flying 3m above the surface of water. To a fish underwater, the height of the bird from the water surface appears to be

Options

A. 2.25m
B. 3.33m
C. 4m
D. 4/3m

Answer

To solve the problem of how high the bird appears to a fish underwater, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given data:**
- The actual height of the bird above the water surface, \( h_{real} = 3 \, \text{m} \).
- The refractive index of air, \( \nu_1 = 1 \).
- The refractive index of water, \( \nu_2 = \frac{4}{3} \).

2. **Use the formula for apparent height:**
The relationship between the real height and the apparent height is given by the formula:
\[ \frac{\nu_1}{\nu_2} = \frac{h_{real}}{h_{apparent}} \]
where \( h_{apparent} \) is the height of the bird as seen by the fish.

3. **Substitute the known values into the formula:**
\[ \frac{1}{\frac{4}{3}} = \frac{3}{h_{apparent}} \]

4. **Cross-multiply to solve for \( h_{apparent} \):**
\[ 1 \cdot h_{apparent} = 3 \cdot \frac{3}{4} \]
\[ h_{apparent} = \frac{9}{4} \]

5. **Convert to decimal form:**
\[ h_{apparent} = 2.25 \, \text{m} \]

6. **Conclusion:**
The height of the bird from the water surface, as perceived by the fish underwater, is \( 2.25 \, \text{m} \).

### Final Answer:
The height of the bird from the water surface appears to be **2.25 meters** to the fish underwater.

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