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

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Detailed Solution

Case 1,

$\frac{μ_{2}}{V} - \frac{μ_{1}}{u} = \frac{μ_{2} - μ_{1}}{R}$

$\Rightarrow \frac{μ_{2}}{- 5} - \frac{1.5}{- 6} = \frac{μ_{2} - 1.5}{- 9} \Rightarrow μ_{2} = \frac{15}{16}$

Case 2,

$\frac{μ_{2}}{V} - \frac{μ_{1}}{u} = \frac{μ_{2} - μ_{1}}{R}$

$\Rightarrow \frac{\frac{15}{16}}{V} - \frac{1.5}{- 12} = \frac{\frac{15}{16} - 1.5}{- 9}$

$\Rightarrow V = - 15 cm$

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