1. Tardigrade
  2. Question
  3. Physics
  4. 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?

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Q. 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?

Ray Optics and Optical Instruments

Solution:

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 $\mu' = 1.94$
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
$8.5-7.99 = 0.51\, cm$