A transparent cube contains a small air bubble. Its apparent distance is 2 cm when seen through other facel. If the refractive index of the material of the cube is 1.5, the real length of the edge of cube must be

Options

A. 3 cm
B. 7.5 cm
C. 10.5cm
D. `14/3` cm

Explanation

To solve the problem, we need to find the real length of the edge of a transparent cube that contains a small air bubble. We are given the apparent distance of the bubble when viewed through the cube and the refractive index of the cube's material.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- Apparent distance (d') of the air bubble = 2 cm
- Refractive index (μ) of the cube's material = 1.5

2. **Use the Formula for Apparent Distance**:
The relationship between the real distance (d) and the apparent distance (d') in a medium with a refractive index (μ) is given by the formula:
\[ d' = \frac{d}{\mu} \]
where:
- \( d' \) = apparent distance
- \( d \) = real distance
- \( μ \) = refractive index

3. **Rearranging the Formula**:
To find the real distance (d), we can rearrange the formula:
\[ d = d' \times μ \]

4. **Substituting the Values**:
Now, substitute the known values into the rearranged formula:
\[ d = 2 \, \text{cm} \times 1.5 \]

5. **Calculating the Real Distance**:
\[ d = 3 \, \text{cm} \]

6. **Conclusion**:
The real length of the edge of the cube is 3 cm.

### Final Answer:
The real length of the edge of the cube must be **3 cm**.