question_answer

A transparent cube of 15 cm edge contains a small air bubble. Its apparent depth when viewed through one face is 6 cm and when viewed through the opposite face is 4 cm. Then the refractive index of the material of the cube is [CPMT 2004; MP PMT 2005]

A)            2.0 

B)            2.5 

C)            1.6 

D)            1.5

Correct Answer: D

Solution :

                   When viewed from face (1) \[\mu =\frac{u}{v}=\frac{x}{v}\]\[=\frac{x}{6}\]                                           .....(i) Now when viewed from face (2) \[\mu =\frac{15-x}{v}=\frac{15-x}{4}\]                                                               .....(ii) From equation (i) and (ii) \[\mu =\frac{15-6\mu }{4}\]\[\Rightarrow \mu =1.5\].