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)  8 3  cm                    (4) 6 cm

Dear student

The observer sees the image due to refraction at the spherical surfacewhen the light from the bubble goes from the glass to the air so n2v-n1u=n2-n1Rwhere n1 is the refractive index of air, n2 is the refractive index of glass, u and v are the real and apparent depths of bubble then1v-1.5-4=1.5-1-101v=0.510-1.54v=-3 cm
So correct option is (1).

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It should be 4 cm as when seen normally so light will be perpendicular to surface of sphere and hence it will not suffer any deflection. If we would see it from some other angle then it would shift. In case the bubble would have been at the center of sphere then no matter from which position we see it, it'll always be at the center as line joining Center And surface of sphere is always perpendicular so it won't refraction hence there will be no change in depth.
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