Question

A tank is filled with water to a height of 15.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 8.5 cm. If water is replaced by a liquid of refractive index 1.94 upto the same height, by what distance would the microscope have to be moved to focus on the needle again ?

• A. 1.00 cm
• B. 2.37 cm
• C. 0.51 cm
• D. 3.93 cm

Answer 1

Answer: (C)

0.51 cm

Actual depth of the needle in water;
$h_1$ = 15.5 cm
Apparent depth of needle in water, $h_2$ = 8.5 cm
For another liquid with $\mu$ = 1.94 cm
Apparent depth,H = $\frac{15.5}{1.94}$ =7.99 cm
Here,H is less than $h_2$ Thus to focus the needle again, the microscope should be moved up by the distance 8.5-7.99 = 0.51 cm