In a pond of water, a flame is held 2 m above the surface of the water. A fish is at depth of 4 m from the water surface. Refractive index of water is `(4)/(3)`. The apparent height of the flame from the eyes of fish is -

Options

A. 5.5 m
B. 6 m
C. `(8)/(3)m`
D. `(20)/(3)m`

Answer

To find the apparent height of the flame from the eyes of the fish, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Height of the flame above the water surface, \( h_1 = 2 \, \text{m} \)
- Depth of the fish below the water surface, \( h_2 = 4 \, \text{m} \)
- Refractive index of water, \( \mu = \frac{4}{3} \)

2. **Calculate the Apparent Height of the Flame Above the Water Surface:**
- The formula for apparent height when viewing from a medium with a different refractive index is given by:
\[ h_1' = \frac{h_1}{\mu} \]
- Substituting the values:
\[ h_1' = \frac{2 \, \text{m}}{\frac{4}{3}} = 2 \times \frac{3}{4} = \frac{6}{4} = \frac{3}{2} \, \text{m} = 1.5 \, \text{m} \]

3. **Determine the Total Apparent Height from the Fish's Perspective:**
- The fish is at a depth of \( 4 \, \text{m} \) below the water surface. Therefore, the total apparent height \( H \) from the fish's eyes to the flame is:
\[ H = h_1' + h_2 \]
- Substituting the values:
\[ H = 1.5 \, \text{m} + 4 \, \text{m} = 5.5 \, \text{m} \]

4. **Final Result:**
- The apparent height of the flame from the eyes of the fish is \( 5.5 \, \text{m} \).

### Summary:
The apparent height of the flame from the eyes of the fish is \( 5.5 \, \text{m} \).