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The radii of two soap bubbles are r(1) a...

The radii of two soap bubbles are `r_(1) and r_(2) (r_(2) lt r_(1))`. They meet to produce a double bubble. The radius of their common interface is

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`becauser_(1)ltr_(2)thereforeP_(1)gtP_(2)` small part of bubbles is in equilibrium
`impliesP_(1)(DeltaA)-P_(2)(DeltaA)=(4T)/(r)DeltaAimplies(4T)/(r_(1))-(4T)/(r_(2))=(4T)/(r)impliesr=(r_(1)r_(2))/(t_(2)-t_(1))``
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