Question

The apparent depth of a needle lying at the bottom of the tank, which is filled with water of refractive index 1.33 to a height of 12.5 cm is measured by a microscope to be 9.4 cm. If water is replaced by a liquid of refractive index 1.63 upto the same height. What distance would the microscope have to be moved to focus on the needle again ?

• A. 1.73 cm
• B. 2.13 cm
• C. 1.5 cm
• D. 2.9 cm

Answer 1

The correct option is A 1.73 cm

Apparent depth = $\frac{Realdepth}{{}^a{\mu }_1}$
Here, Real depth=12.5 cm and ${}^a{\mu }_1$ = 1.63
$\therefore$ Apparent depth = $\frac{12.5}{1.63}$ =7.67 cm
Now the microscope will have to shift from its initial position to focus 9.4 cm depth object to focus 7.67 cm depth object.
Shift distance = 9.4-7.67=1.73 cm