# Half filled glass of water

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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