Question

A small air bubble is inside a transparent cube of side length $24\text{cm}$ and of refractive index $\frac{4}{3}$. If the apparent distance of air bubble when viewed from top of one of the faces is $9\text{cm}$, then its apparent distance when viewed from opposite face will be

• A. $6\text{cm}$
• B. $8\text{cm}$
• C. $9\text{cm}$
• D. $7\text{cm}$

Answer 1

The correct option is C $9\text{cm}$

Side length of the cube $=$ thickness of the cube, $t=24\text{cm}$
Let real depth of air bubble when viewed from top of one of the faces be $d_1$ and apparent depth be $d_{app}=9\text{cm}$
So, $\mu =\frac{d_{real}}{d_{app}}$
or, $\frac{4}{3}=\frac{d_1}{9}$
$\therefore d_1=12\text{cm}$



When viewed from the opposite face,
$d_{real}=d_2=t-d_1=24-12=12\text{cm}$
Now, $\mu =\frac{d_2}{d_{app}}$
$\Rightarrow d_{app}=\frac{12\times 3}{4}=9\text{cm}$

Why this question? Tips: Sum of the real depths of bubble from both faces is equal to thickness of the cube or medium.