An air bubble is situated at a distance of 0.08 m from the centre of a sphere of radius 0.12 m. When viewed from the nearest side it appears to be distance of 0.09 m from the centre. Find the refractive index of the material of the sphere. Where will the bubble appear to be when viewed from the farther side?

Explanation

Object distance of the air bubble from `P_(1)`
`-u=0.12-0.08=0.04m ` for real object.
`r_(1)=0.12 m (P_(1)O)`
`v=-(0.12-0.09)`
i.e., `v=-0.03 m (P_(1)B)`
(i) using the formula `(n_(0))/(-u)+(n_(1))/(v)= (n_(0)-n_(1))/(r)`
.v. is negative because it is measured opposite to the direction of incident light.
`(n_(0))/(0.04)+(1)/(-0.03)=(n_(0)-1)/(0.12)`
`25n_(0)-33.33=(n_(0)-1)8.33`
`25n_(0)-8.33n_(0)=33.33-8.33`
`16.67n_(0)-25`
`therefore n_(0)=1.4997`
`n_(0)=1.50`

(ii) u from `P_(2)=(0.12+0.08)=0.20m`
`(1.5)/(0.2)+(1)/(v)=(1.5-1)/(0.12)`
`7.5+(1)/(v)=4.167`
`therefore (1)/(v)=-3.333`
`therefore v= -(1)/(3.333)= -(1)/(10//3)`
or `v=(-3)/(10)=-0.30m`