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  4. A microscope is focused on a coin lying at the bottom of a beaker. The microscope is now raised up by 1 cm. To what depth should the water be poured into the beaker so that coin is again in focus? (Refractive index of water is (4/3) )

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Q. A microscope is focused on a coin lying at the bottom of a beaker. The microscope is now raised up by $ 1\, cm$. To what depth should the water be poured into the beaker so that coin is again in focus? (Refractive index of water is $ \frac{4}{3} $ )

UPSEEUPSEE 2010Ray Optics and Optical Instruments

Solution:

Water should be poured to a height $h \,cm$ so that apparent shift in position of coin is $1\, cm$. As $y=\left(1-\frac{1}{n}\right) h$
$\Rightarrow h=\frac{y}{\left(1-\frac{1}{n}\right)}=\frac{1}{\left(1-\frac{1}{4 / 3}\right)}=\frac{1}{\frac{1}{4}}=4\, cm$