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

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Real depth = 12.5 cm, Apparent depth = 9.4 cm

refractive index of water, µ = Real depth/Apparent depth = 12 .5/9.4 = 1.33

When the water is replaced by a liquid of refractive index (µ = 1.63), real depth = 12.5 cm apparent depth = ?

µ = Real depth/Apparent depth

Apparent Depth = Real depth/µ = 12.5/1.63 = 7.7cm

The microscope has to be moved to focus on the needle through a distance of (9.4 – 7.7) = 1.7cm

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