The point of constructive interference has intensity 4A^2. But you can find another spot
where the intensity is zero. Does energy conversion hold up? Yes it does, and one nice
way to see it is in the distant interference pattern of two very narrow slits.
Very far from the slits along their perpendicular bisector the intensity is 4A^2. At other
angles very far from the slits (assuming equal amplitudes A due to each slit) the intensity
depends on the cosine squared of half the phase difference between the waves. You find
out that the average intensity is 2A^2 when all is said and done, just like you expect from
energy conservation.
Mike
Mike Moloney, Dept of Physics & Applied Optics, Rose-Hulman Institute of Technology