Question

A small air bubble is trapped inside a transparent cube of size $12\text{cm}$. When viewed from one of the vertical faces, the bubble appears to be at $5\text{cm}$ from it. When viewed from opposite face, it appears at $3\text{cm}$ from it.

• A. The distance of the air bubble from the first face is $7.5\text{cm}$
• B. The distance of the air bubble from the first face is $9\text{cm}$
• C. Refractive index of the material of the cube is $2.0$.
• D. Refractive index of the material of the cube is $1.5$.

Answer 1

Answer: (A), (D)

Refractive index of the material of the cube is $1.5$.


Let the bubble $B$ be at distance $H$ from the face $F_1$ of the cube.

$h_1=\frac{n_a}{n_C}H=5\text{cm}$

Similarly when looking from opposite face $F_2$,
$h_2=\frac{n_a}{n_C}(12-H)=3\text{cm}$

Solving $H=7.5\text{cm}$ and $n_C=1.5$