question_answer

A transparent cube of 0.21 m edge contains a small air bubble. Its apparent distance when viewed through one face of the cube is 0.10 m and when viewed from the opposite face if 0.04 m. The actual distance of the bubble from the second face of the cube is

A) 0.06 m                                  

B) 0.17 m          

C) 0.05 m                  

D) 0.04 m        

Correct Answer: A

Solution :

\[\text{Refractive index =}\frac{\text{real depth}}{\text{apparent depth}}\] \[\therefore \]        \[\frac{x}{0.04}=\frac{0.21-x}{0.10}\] \[\Rightarrow \]     \[0.21\times 0.04-x\times 0.04=0.10x\] \[\Rightarrow \]      \[x=\frac{0.21\times 0.04}{0.14}=0.06\,m\]