Question

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

• A. The distance of the air bubble from the first face is 7.5 cm.
• B. The distance of the air bubble from the first face is 9 cm.
• C. Refractive index of the material of the prism is 2.0.
• D. Refractive index of the material of the prism is 1.5.

Answer 1

Answer: (A), (D)

The distance of the air bubble from the first face is 7.5 cm.
Refractive index of the material of the prism is 1.5.

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

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

Similarly when looking from opposite face $F_2$,

$h_2=\frac{n_a}{n_C}(12-H)=3cm$
Solving the two equations, we get

$H=7.5cm$ and $n_c=1.5$