1. Set up the geometry

Let the real distance of the bubble from one face be $x$. Then its distance from the opposite face is $24 - x$ because the side of the ice cube is $24\,\text{cm}$.

2. Use apparent depth formula

For an object inside a denser medium viewed from air, $\text{apparent depth} = \frac{\text{real depth}}{\mu}$ where $\mu$ is the refractive index of ice.

3. Observation from the first side

Apparent distance is $12\,\text{cm}$, so $\frac{x}{\mu} = 12$ Hence, $x = 12\mu$

4. Observation from the opposite side

Apparent distance is $4\,\text{cm}$, so $\frac{24-x}{\mu} = 4$ Hence, $24 - x = 4\mu$

5. Substitute $x = 12\mu$

$24 - 12\mu = 4\mu$ $24 = 16\mu$ $\mu = \frac{24}{16} = \frac{3}{2}$

6. Check with options

$\mu = \frac{3}{2}$ So the correct option is A.