A hemispherical glass body of radius 20cm and refractive index 1.5 is silvered on its curved surface. A small air bubble is 4 cm below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen ____cm below flat surface.

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answer is 10.

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Detailed Solution

$\begin{array}{l} \frac{1}{F} = \frac{1}{ϑ} + \frac{1}{μ} \Rightarrow \frac{1}{- 10} = \frac{1}{ϑ} + \frac{1}{- 6} \\ = \frac{1}{ϑ} = - \frac{1}{10} + \frac{1}{6} = \frac{- 6 + 10}{60} = \frac{4}{60} = \frac{1}{15} \\ ϑ = 15 c m \\ ϑ^{1} = \frac{ϑ}{μ} = \frac{15}{3 / 2} = 10 c m \end{array}$

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