Question

# A glass sphere $$(\mu = 1.5)$$ of radius $$20\ cm$$ has a small air bubble $$4\ cm$$ below its center. The sphere is viewed from outside and along a vertical line through the bubble. The apparent depth of the bubble below the surface of sphere is (in cm) :

A
13.33
B
26.67
C
15
D
30

Solution

## The correct option is B $$26.67$$concept: It is the case of refraction through curved surface formulae used$$\dfrac{\mu_2}{v}-\dfrac{\mu_1}{u}=\dfrac{\mu_2-\mu_1}{R}$$Given: $$\mu_2=1$$, $$\mu_1=1.5$$$$R=-20$$Object distance$$=u=-(20+4)=-24$$Here apparent depth is image distance which is v$$\dfrac{1}{v}-\dfrac{1.5}{-24}=\dfrac{1-1.5}{-20}$$$$\Rightarrow \dfrac{1}{v}=\dfrac{1}{40}-\dfrac{1}{16}=\dfrac{-3}{80}$$$$\Rightarrow v=-\dfrac{80}{3}=-26.67$$Hence bubble looks at depth of $$26.67$$.Physics

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