A small air bubble is situated at a distance of 3 cm from the centre of a glass sphere of radius 9 cm. When viewed from the nearest side, the bubble appears to be at a distance of 5 cm from the surface. Its apparent distance when viewed from the farthest side is $n \times 5 c m$ where ' $n$ ' is?

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answer is 3.

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Detailed Solution

For the refraction at $P_{1}; μ_{1} = μ, μ_{2} = 1, u = - 6 c m$

$v = - 5 c m, R = - 9 c m$

$\begin{array}{l} \frac{μ_{2}}{v} - \frac{μ_{1}}{u} = \frac{μ_{2} - μ_{1}}{R} \\ \frac{1}{- 5} - \frac{μ}{- 6} = \frac{1 - μ}{- 9} \\ μ = \frac{8}{5} = 1.6 \end{array}$

For the refraction at $P_{2}$

$μ_{1} = 1.6, μ_{2} = 1, u = - 12 c m, R = - 9 c m$

$\begin{array}{l} \frac{μ_{2}}{v} - \frac{μ_{1}}{u} = \frac{μ_{2} - μ_{1}}{R} \\ \frac{1}{v} - \frac{1.6}{- 12} = \frac{1 - 1.6}{- 9} \\ v = 15 c m . \\ n \times 5 = 15 \Rightarrow n = 3 \end{array}$