A small air bubble is inside a transparent cube of side length 24 cm and of refractive index `4/3` If the apparent distance air bubble from a face is 9 cm then its apparent distance from opposite face is

Options

A. 6cm
B. 8cm
C. 9cm
D. 12cm

Explanation

To solve the problem, we need to determine the apparent distance of the air bubble from the opposite face of the cube. We will use the concept of apparent depth in optics.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Side length of the cube, \( L = 24 \, \text{cm} \)
- Refractive index of the cube, \( n_1 = \frac{4}{3} \)
- Apparent distance of the bubble from one face, \( d_{\text{apparent}} = 9 \, \text{cm} \)

2. **Understand the Geometry:**
- The cube has a total depth of 24 cm. If the bubble is located at a certain depth, we can denote its actual depth from one face as \( d_{\text{actual}} \) and from the opposite face as \( L - d_{\text{actual}} \).

3. **Use the Formula for Apparent Depth:**
- The formula for apparent depth is given by:
\[ \frac{n_2}{d_{\text{apparent}}} = \frac{n_1}{d_{\text{actual}}} \]
- Where \( n_2 \) is the refractive index of air (approximately 1) and \( n_1 \) is the refractive index of the cube.

4. **Calculate the Actual Depth:**
- Rearranging the formula to find \( d_{\text{actual}} \):
\[ d_{\text{actual}} = \frac{n_1 \cdot d_{\text{apparent}}}{n_2} \]
- Substituting the known values:
\[ d_{\text{actual}} = \frac{\frac{4}{3} \cdot 9}{1} = 12 \, \text{cm} \]

5. **Determine the Apparent Distance from the Opposite Face:**
- The actual depth from one face is 12 cm. Therefore, the distance from the opposite face is:
\[ d_{\text{opposite}} = L - d_{\text{actual}} = 24 \, \text{cm} - 12 \, \text{cm} = 12 \, \text{cm} \]
- Now, we can find the apparent distance from the opposite face using the same formula:
\[ d_{\text{apparent, opposite}} = \frac{n_2 \cdot d_{\text{actual}}}{n_1} \]
- Substituting the values:
\[ d_{\text{apparent, opposite}} = \frac{1 \cdot 12}{\frac{4}{3}} = 9 \, \text{cm} \]

### Conclusion:
The apparent distance of the air bubble from the opposite face of the cube is **9 cm**.