Prove that if two bubbles of radii `r_(1)` and `r_(2)(r_(1)ltr_(2))` come in contact with each other then the radius of curvature of the common surface `r=(r_(1)r_(2))/(r_(2)-r_(1))`

Answer

`r=(r_(1)r_(2))/(r_(1)-r_(2))`

Explanation

`(4S)/(r )= (4S)/(r_(2))-(4S)/(r_(1))`
`(1)/(r )= (1)/(r_(2))-(1)/(r_(1))`
`r=(r_(1)-r_(2))/(r_(1)r_(2))`