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Q.

A concave mirror is placed at the bottom of an empty tank with face upwards and axis vertical. When sunlight falls normally on the mirror, it is focused at distance of 32 cm from the mirror. If the tank is filled with water $(μ = \frac{4}{3})$ upto a height of 20 cm, then find the height above water surface (in cm) at which the sunlight will now get focused at

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answer is 9.

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Detailed Solution

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When water is filled in the tank upto a height of 20 cm, the image formed by the mirror will act as virtual object for water surface. Which will form it’s image at/such that $\frac{A c t u a l h e i g h t}{A p p e r a n t h e i g h t} = \frac{μ_{w}}{μ_{a}} i . e \frac{B O}{B I} = \frac{4 / 3}{1}$

$\Rightarrow B I = B O \times \frac{3}{4} = 12 \times \frac{3}{4} = 9 c m$

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