When two soap bubbles of radii a and
b(b>a) coalesce, it can be shown as follows
Pressure inside the bubble
1,p1=p0+‌ where,
p0 is the initial pressure,
T is the surface tension
and
a is the radius of the bubble
1. Similarly, pressure inside the bubble
2,p2=p0+‌ where,
b is the radius of the bubble 2 .
Excess pressure at common surface is given by
p‌ex ‌=p1−p2 Let,
r be the radius of common surface, then
⇒‌‌‌=(p0+‌)−(p0+‌) ⇒‌‌‌=p0+‌−p0−‌ ⇒r=‌, which is the required expression for radius of curvature at common surface.