An object is placed at 24 cm distant from a surface of a lake. If water has refractive index of `4//3`, then at what distance from the lake surface, a fish will get sight of an object.

Options

A. 32 cm above the surface of water
B. 18 cm over the surface of water
C. 6 cm over the surface of water
D. 6 cm below the surface of water

Answer

To solve the problem, we will use the formula that relates the apparent depth (d') and the real depth (d) of an object when viewed from a different medium, which is given by the refractive index (μ) of the medium:

\[ \mu = \frac{\text{Apparent Depth (d')}}{\text{Real Depth (d)}} \]

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Real depth (d) = 24 cm
- Refractive index (μ) = \( \frac{4}{3} \)

2. **Write the Formula:**
- The formula relating apparent depth and real depth is:
\[ \mu = \frac{d'}{d} \]
Rearranging this gives:
\[ d' = \mu \times d \]

3. **Substitute the Known Values:**
- Substitute the values of μ and d into the formula:
\[ d' = \frac{4}{3} \times 24 \text{ cm} \]

4. **Calculate the Apparent Depth:**
- Perform the multiplication:
\[ d' = \frac{4 \times 24}{3} = \frac{96}{3} = 32 \text{ cm} \]

5. **Conclusion:**
- The fish will see the object at an apparent depth of 32 cm from the surface of the lake.

### Final Answer:
The distance from the lake surface at which the fish will see the object is **32 cm**.

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