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 is 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 :

Refractive index \[=\frac{real\text{ }depth}{apparent\text{ }depth}\] \[\therefore \]  \[\frac{x}{0.04}=\frac{0.21-x}{0.10}\] \[\Rightarrow \]               \[0.21\times 0.04-x\times 0.4=0.10x\] \[\Rightarrow \]               \[x=\frac{0.21\times 0.04}{0.14}=0.06\,m\]