A bird in air looks at a fish vertically below it and inside water. `h_(1)` is the height of the bird above the surface of water and `h_(2)`, the depth of the fish below the surface of water. If refractive index of water with respect to air be `mu`, then the distance of the fish as observed by the bird is

Options

A. `h_(1)+h_(2)`
B. `h_(1)+(h_(2))/(mu)`
C. `muh_(1)+h_(2)`
D. `muh_(1)+muh_(2)`

Explanation

To solve the problem step by step, we need to determine the distance of the fish as observed by the bird, taking into account the refractive index of water.

### Step 1: Understand the Setup
We have a bird flying in the air at a height \( h_1 \) above the surface of the water and a fish located at a depth \( h_2 \) below the water surface. The refractive index of water with respect to air is given as \( \mu \).

### Step 2: Determine Actual Distance
The actual distance between the bird and the fish can be calculated as the sum of the height of the bird above the water and the depth of the fish below the water:
\[ \text{Actual Distance} = h_1 + h_2 \]

### Step 3: Calculate Apparent Depth of the Fish
When the bird looks down into the water, the fish appears to be at a different depth due to the refraction of light. The apparent depth \( h_{2, \text{apparent}} \) of the fish as seen by the bird can be calculated using the formula:
\[ h_{2, \text{apparent}} = \frac{h_2}{\mu} \]
This formula indicates that the apparent depth is less than the actual depth because \( \mu \) (the refractive index of water) is greater than 1.

### Step 4: Combine Heights for Apparent Distance
The total apparent distance \( D \) that the bird perceives to the fish is the sum of the height of the bird above the water and the apparent depth of the fish:
\[ D = h_1 + h_{2, \text{apparent}} = h_1 + \frac{h_2}{\mu} \]

### Step 5: Final Expression
Thus, we can express the apparent distance of the fish as observed by the bird:
\[ D = h_1 + \frac{h_2}{\mu} \]

### Conclusion
The distance of the fish as observed by the bird is given by:
\[ D = h_1 + \frac{h_2}{\mu} \]