A fish lies at the bottom of a `4`m deep water lake. A bird flies 6m above the water surface and refractive index of water is `4//3` . Then the distance between

Options

A. Bird and image of fish is 9m
B. Fish and image of is 12m
C. Fish and image of bird is 8m
D. Fish and image of bird is 10m

Explanation

To solve the problem step by step, we will calculate the apparent depth of the fish and the apparent height of the bird, and then find the distances between the images and the actual objects.

### Step 1: Understand the situation
- The fish is located at the bottom of a lake that is 4 meters deep.
- The bird is flying 6 meters above the water surface.
- The refractive index of water (μ) is given as \( \frac{4}{3} \).

### Step 2: Calculate the apparent depth of the fish
The formula for apparent depth (d') when light travels from a medium of refractive index \( \mu_1 \) (water) to \( \mu_2 \) (air) is given by:
\[ d' = d \times \frac{\mu_2}{\mu_1} \]
where:
- \( d \) is the real depth (4 m),
- \( \mu_1 = \frac{4}{3} \) (for water),
- \( \mu_2 = 1 \) (for air).

Substituting the values:
\[ d' = 4 \times \frac{1}{\frac{4}{3}} = 4 \times \frac{3}{4} = 3 \text{ m} \]

### Step 3: Calculate the distance between the image of the fish and the bird
The distance between the image of the fish and the bird can be calculated by adding the height of the bird above the water surface and the apparent depth of the fish:
\[ \text{Distance} = \text{Height of Bird} + \text{Apparent Depth of Fish} \]
Substituting the values:
\[ \text{Distance} = 6 \text{ m} + 3 \text{ m} = 9 \text{ m} \]

### Step 4: Calculate the apparent height of the bird
Using the same formula for apparent height:
\[ h' = h \times \frac{\mu_1}{\mu_2} \]
where:
- \( h \) is the real height (6 m),
- \( \mu_1 = \frac{4}{3} \) (for water),
- \( \mu_2 = 1 \) (for air).

Substituting the values:
\[ h' = 6 \times \frac{\frac{4}{3}}{1} = 6 \times \frac{4}{3} = 8 \text{ m} \]

### Step 5: Calculate the distance between the image of the bird and the fish
The distance between the image of the bird and the fish can be calculated by adding the apparent height of the bird and the real depth of the fish:
\[ \text{Distance} = \text{Apparent Height of Bird} + \text{Real Depth of Fish} \]
Substituting the values:
\[ \text{Distance} = 8 \text{ m} + 4 \text{ m} = 12 \text{ m} \]

### Final Results
- The distance between the image of the fish and the bird is **9 meters**.
- The distance between the image of the bird and the fish is **12 meters**.