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There is a small air bubble inside a glass sphere (µ = 1.5) of radius 10 cm. The bubble is 4 cm below the surface and is viewed normally from outside. The apparent depth of the bubble is

(1) 3 cm (2) 4 cm (3) $\frac{8}{3}$ cm (4) 6 cm

$Theobserverseestheimageduetorefractionatthesphericalsurface\phantom{\rule{0ex}{0ex}}whenthelightfromthebubblegoesfromtheglasstotheairso\phantom{\rule{0ex}{0ex}}\frac{{n}_{2}}{v}-\frac{{n}_{1}}{u}=\frac{{n}_{2}-{n}_{1}}{R}\phantom{\rule{0ex}{0ex}}where{n}_{1}istherefractiveindexofair,{n}_{2}istherefractiveindexofglass,uandv\phantom{\rule{0ex}{0ex}}aretherealandapparentdepthsofbubblethen\phantom{\rule{0ex}{0ex}}\frac{1}{v}-\frac{1.5}{-4}=\frac{1.5-1}{-10}\phantom{\rule{0ex}{0ex}}\frac{1}{v}=\frac{0.5}{10}-\frac{1.5}{4}\phantom{\rule{0ex}{0ex}}v=-3cm$

So correct option is (1).

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