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An air bubble in a glass sphere (mu = 1....

An air bubble in a glass sphere `(mu = 1.5)` is situated at a distance 3 cm from a convex surface of diameter 10 cm. At what distance from the surface will the bubble appear ?

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In case of refraction from curved surface `(mu_(2))/(v) -(mu_(1))/(u) = ((mu_(2)-mu_(1))/(R)`
(a) " " `mu_(1) = 1.5 , mu_(2) = 1 , R = -5"cm" "and" u=-3 "cm" implies (1)/(v)- ((1.5))/((-3)) = (1-1.5)/((-5)) implies v=-2.5 "cm"` the bubble will appear at a distance `2.5"cm"` from the convex curved surface inside the glass.
(b) `mu_(1) = 1.5 , mu_(2) =1 , R =5 "cm" "and" u = -3 "cm" implies (1)/(v)- ((1.5))/((-3)) = (1-1.5)/((5)) implies v= -1.66 "cm"`
the bubble will appear at a distance `1.66` cm from the concave curved surface inside the glass .
Note: If the surface is plane then `R rarr oo`
case(a) or (b) would yield `(1)/(v) - ((1.5))/((-3)) = ((1 - 1.5))/(oo) implies v= -2"cm"`
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