A point source of light is kept at the bottom of a cylindrical container of radius \(R\), half filled with water. It is seen that light emerges out of the top surface of water from a circular area of radius \(r (<R)\).

If water is poured in the container at a rate \(\frac{dV}{dt} = Q \) then the radius of circular area will change at the rate \(\frac{\sqrt{a}Q}{\sqrt{b}\pi R^2}\) where \(a\) and \(b\) are coprime positive integers, find the value of \(a+b\).

Take the refractive index of water as \(\frac{4}{3}\).

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