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 mircoscope have to be moved to focus on the needle again?

Solution

Case I: When tank is filled with water.

Given, real depth = 12.5 cm;
apparent depth = 9.4 cm

Now, using the formula,

μ = \frac{real depth}{apparent depth}

we have,
Refractive index,

μ = \frac{12.5}{9.4} = 1.33

Case II: When water in the tank is replaced by another liquid.

Refractive index of liquid, μ = 1.63 Real depth = 12.5 cm

Therefore,

apparent depth = \frac{real depth}{μ}

i.e.,

apparent depth = \frac{12.5}{1.63} = 7.67 cm

Distance through which microscope has to be moved downward is = (9.4 – 7.67) cm = 1.73 cm.

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