question_answer

A tank is filled with water to a height of 12.4 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.3 cm. If water is replaced by a liquid of refractive index 1.6 upto the same height, by what distance would the microscope have to be moved to focus on the needle again

A)  4cm                                      

B)  3cm

C)  2.18 cm               

D)  2.05 cm

E)  None of these above

Correct Answer: E

Solution :

The relationship between refractive index u. real depth and apparent depth is \[\mu =\frac{Real\text{ }depth}{Apparent\text{ }depth}=\frac{12.4\,cm}{9.3\,cm}=\frac{4}{3}\] For another liquid, \[\mu =1.6\] \[\mu =\frac{Real\text{ }depth}{Apparent\text{ }depth}\] Or           \[1.6=\frac{12.4\,cm}{Apparent\text{ }depth}\] Apparent depth\[=\frac{12.4}{1.6}\] \[=7.75cm\] Distance moved by microscope \[=9.3-7.75=1.55\text{ }cm\]