Step 1: Understanding the Concept:
Refractive index $\mu = \frac{\text{Real Depth}}{\text{Apparent Depth}}$.
Step 2: Formula Application:
Let the real distance of the bubble from the first face be $x$. Then from the second face, it is $21 - x$.
$\mu = \frac{x}{d_1}$ and $\mu = \frac{21 - x}{d_2}$, where $d_1, d_2$ are apparent depths.
Step 3: Explanation:
Sum of real depths = Total thickness = 21 cm.
$\mu \cdot d_1 + \mu \cdot d_2 = 21 \implies \mu(d_1 + d_2) = 21$.
Given $d_2$ (from opposite face) is 6 cm. Let's find $\mu$ using the sum.
If the bubble appears at 6 cm from one side and 8 cm from the other (assumed logic for standard 1.5 index), then $\mu = 21 / (d_1 + d_2)$.
Using Option D values: If $x = 9$, then $\mu = 9/6 = 1.5$. From other side, real depth is $21-9=12$. Apparent depth $= 12/1.5 = 8$. (Question text mentions 6 cm from opposite face). Let's re-verify: if $\mu=1.5$ and total real is 21, total apparent is $21/1.5 = 14$. If one side is 6, the other must be 8.
Step 4: Final Answer:
The refractive index is 1.5 and actual distance is 9 cm (or 12 cm depending on which face is "first").