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\[=\frac{real\,\,depth}{apparent\,\,depth}\] \[\therefore \]  \[\frac{x}{0.04}=\frac{0.21-x}{0.10}\] \[\Rightarrow \]               \[0.12\times 0.04-x\times 0.04=0.10x\] \[\Rightarrow \]               \[x=\frac{0.21\times 0.04}{0.14}=0.06\,\,m\]