A fish at a depth of `12 cm ` in water is viewed by an observer on the bank of a lake. To what height the images of the fish is raised ?

Options

A. `9 cm`
B. `12 cm`
C. `3.8 cm`
D. `3 cm`

Explanation

To solve the problem of how much the image of a fish at a depth of 12 cm in water is raised when viewed by an observer on the bank of a lake, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Actual depth of the fish (d_actual) = 12 cm
- Refractive index of water (μ) = 4/3

2. **Use the Formula for Apparent Depth:**
The formula for apparent depth (d_apparent) when viewing an object submerged in a medium is given by:
\[ d_{apparent} = \frac{d_{actual}}{\mu} \]

3. **Substitute the Given Values into the Formula:**
Substitute the actual depth and the refractive index into the formula:
\[ d_{apparent} = \frac{12 \, \text{cm}}{\frac{4}{3}} \]

4. **Calculate the Apparent Depth:**
To simplify the calculation:
\[ d_{apparent} = 12 \times \frac{3}{4} = 9 \, \text{cm} \]

5. **Determine the Height the Image is Raised:**
The height the image of the fish is raised can be found by subtracting the apparent depth from the actual depth:
\[ \text{Height raised} = d_{actual} - d_{apparent} = 12 \, \text{cm} - 9 \, \text{cm} = 3 \, \text{cm} \]

6. **Conclusion:**
The image of the fish is raised by 3 cm.

### Final Answer:
The image of the fish is raised by **3 cm**.

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