A large squre container with thin transparent vertical walls and filled with water ( refractive index `(4)/(3)`) is kept on a horizontal table . A student holds a thin straight wire vertically inside the water 12cm from one of its corners, as shown schematically in the figure . Looking at the inside the water 12 cm from one of its corners, as shown schematically in the figure . Looking at the wire from this corner, another student sees two images of the wire , located symmetrically on each side of the line of sight as shown. THe separation (in cm) between these images is _______ .

Explanation

To solve the problem, we need to determine the separation between the two images of the wire as seen by the student looking from the corner of the square container filled with water. The refractive index of water is given as \( \frac{4}{3} \).

### Step-by-Step Solution:

1. **Understanding the Setup**:
- The wire is placed vertically inside the water at a distance of 12 cm from one of the corners of the square container.
- The observer is looking from the corner of the container, and due to refraction, two images of the wire are formed.

2. **Visualizing the Geometry**:
- The distance from the corner to the wire is 12 cm.
- The line of sight from the observer to the wire will create a right triangle with the water's surface.

3. **Calculating the Apparent Depth**:
- The apparent depth \( O' \) can be calculated using the formula:
\[ O' = \frac{O}{\mu} \]
where \( O \) is the actual depth (12 cm in this case) and \( \mu \) is the refractive index of water (\( \frac{4}{3} \)).
- Thus,
\[ O' = \frac{12 \text{ cm}}{\frac{4}{3}} = 12 \times \frac{3}{4} = 9 \text{ cm} \]

4. **Finding the Distance to the Images**:
- The distance from the observer to the apparent position of the wire is 9 cm.
- The observer sees two images of the wire due to refraction at the water's surface.

5. **Calculating the Separation Between Images**:
- The separation between the two images can be found using the geometry of the situation.
- The distance from the observer to the apparent position of the wire is \( 9 \text{ cm} \).
- The distance from the observer to the images will be symmetric about the line of sight.
- The separation \( D \) between the two images is given by:
\[ D = 2 \times (12 \text{ cm} - 9 \text{ cm}) = 2 \times 3 \text{ cm} = 6 \text{ cm} \]

6. **Final Answer**:
- The separation between the two images of the wire is \( 6 \text{ cm} \).