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 :

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