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?

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

Tardigrade Admin · Accepted Answer

Actual depth of the needle in water, h1 = 15.5 cm Apparent depth of needle in water, h2 = 8.5 cm For another liquid with μ' = 1.94 Apparent depth, H = (15.5/1.94) = 7.99 cm Here, H is less than h2. Thus to focus the needle again, the microscope should be moved up by the distance 8.5-7.99 = 0.51 cm

$1.00 c m$

$2.37 c m$

$0.51 c m$

$3.93 c m$

1.00cm

2.37cm

0.51cm

3.93cm

Actual depth of the needle in water, h1​=15.5cm Apparent depth of needle in water, h2​=8.5cm For another liquid with μ′=1.94 Apparent depth, H=1.9415.5​=7.99cm Here, H is less than h2​. Thus to focus the needle again, the microscope should be moved up by the distance 8.5−7.99=0.51cm

$1.00 c m$

$2.37 c m$

$0.51 c m$

$3.93 c m$