An air bubble in glass `(mu=3//2)` is situated at a distance of 2 cm from centre of sphere of diameter 10 cm. Locate the image of bubble from (a) nearer surface and (b) farther surface.

Explanation

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(a). From nearer surface:
`mu_1=(3)/(2),mu_2=1.0,u=-3cm,R=-5cm,v=?`
`(mu_2)/(v)-(mu_1)/(u)=(mu_2-mu_1)/(R)`
`(1)/(v)-((3)/(2))/(-3)=(1-(3)/(2))/(-5)implies(1)/(v)+(1)/(2)=(1)/(10)`
`(1)/(v)=-(1)/(2)+(1)/(10)=(-5+1)/(10)impliesv=-2.5cm`
The bubble appears nearer from the nearer surface.
(b) From farther surface:
`mu_1=(3)/(2),mu_2=1,u=-(2+5)=7cm`
`R=-5cm,v=?`
`(mu_2)/(v)-(mu_1)/(u)=(mu_2-mu_1)/(R)implies(1)/(v)-(1)/(-7)=(1-(3)/(2))/(-5)`
`(1)/(v)=(1)/(10)-(1)/(7)=(-3)/(70)`
`v=(-70)/(3)=-23.3cm`
The bubble appears farther from the farther surface. If bubble is at centre, it will appear at centre.