A fish which is at a depth of 12 cm in water `(mu = (4)/(3))` is viewed by an observer on the bank of a lake. Its apparent depth as observed by the observer is :

Options

A. 3 cm
B. 9 cm
C. 12 cm
D. 16 cm

Answer

To find the apparent depth of the fish as observed by the observer on the bank of the lake, we can use the formula that relates the real depth, apparent depth, and the refractive index of the medium:

\[ \mu = \frac{\text{Real Depth}}{\text{Apparent Depth}} \]

Where:
- \(\mu\) is the refractive index of water,
- Real Depth is the actual depth of the fish,
- Apparent Depth is the depth at which the fish appears to be located when viewed from above the water.

### Step-by-Step Solution:

1. **Identify the given values:**
- Real Depth (d) = 12 cm
- Refractive Index (\(\mu\)) = \(\frac{4}{3}\)

2. **Use the formula for refractive index:**
\[ \mu = \frac{\text{Real Depth}}{\text{Apparent Depth}} \]
Substituting the known values:
\[ \frac{4}{3} = \frac{12 \text{ cm}}{\text{Apparent Depth}} \]

3. **Rearranging the formula to find Apparent Depth:**
\[ \text{Apparent Depth} = \frac{\text{Real Depth}}{\mu} \]
Substituting the values:
\[ \text{Apparent Depth} = \frac{12 \text{ cm}}{\frac{4}{3}} \]

4. **Calculating Apparent Depth:**
- To divide by a fraction, multiply by its reciprocal:
\[ \text{Apparent Depth} = 12 \text{ cm} \times \frac{3}{4} \]
\[ \text{Apparent Depth} = \frac{36 \text{ cm}}{4} = 9 \text{ cm} \]

5. **Conclusion:**
The apparent depth of the fish as observed by the observer is **9 cm**.

### Final Answer:
The apparent depth of the fish is **9 cm**.

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