A fish is swimming in a pool whose bottom surface is silver polished. Find where an observer in the air will observe the image of the fish if the depth of the pool is H and the fish is at depth h below the water surface?

Options

A. `(H - h)/mu`
B. `2(H - h)/mu`
C. `(H + h)/mu`
D. `(2H - h)/mu`

Answer

To solve the problem of finding where an observer in the air will observe the image of the fish swimming in a pool with a silver polished bottom, we can follow these steps:

### Step 1: Understand the Depths
Let:
- \( H \) = Total depth of the pool
- \( h \) = Depth of the fish below the water surface
- The real depth of the fish from the observer's perspective is \( h \).

### Step 2: Determine the Apparent Depth
The apparent depth \( X_1 \) of the fish can be calculated using the formula:
\[ X_1 = \frac{h}{\mu} \]
where \( \mu \) is the refractive index of water (approximately 1.33 for water).

### Step 3: Calculate the Apparent Depth of the Bottom Surface
The apparent depth \( X_2 \) of the bottom surface (silver polished) can be calculated as:
\[ X_2 = \frac{H}{\mu} \]

### Step 4: Find the Distance Between the Image of the Fish and the Observer
The image of the fish will appear at a distance from the observer equal to the difference between the apparent depth of the bottom surface and the apparent depth of the fish:
\[ \text{Distance to image of fish} = X_2 - X_1 \]

### Step 5: Substitute the Values
Substituting the expressions for \( X_1 \) and \( X_2 \):
\[ \text{Distance to image of fish} = \frac{H}{\mu} - \frac{h}{\mu} \]
This simplifies to:
\[ \text{Distance to image of fish} = \frac{H - h}{\mu} \]

### Step 6: Final Expression
Thus, the observer will see the image of the fish at a distance of:
\[ \text{Distance to image of fish} = \frac{H - h}{\mu} \]

### Summary
The observer will see the image of the fish at a distance of \( \frac{H - h}{\mu} \) above the water surface.

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