Photons

Physics question.

In the famous two slit experiment, light shining through two slits forms interference patterns on the backdrop. So we have standard wave interference: constructive interference where the peaks conincide with peaks and valleys coincide with valleys, and destructive interference when the peaks meet up with the valleys, and vice versa.

Imagine a coherent light source, where all the light is one frequency (color) and all the waves are in phase with each other, like from a laser. Split the beam in two (using one of those magic beam splitters that are ubiquitous to optical experiments), route one of the two beams through a miniscularly longer route so that it is exactly out of phase with the other beam. Now combine the two. These two beams are now completely out of phase and should cancel each other out, right?

Where does the energy go? The light coming out of the laser has a certain amount of energy, but now that we have split the beam, phase shifted half of it, and recombined them, they have disappeared. So where did they go?

For that matter, why do we have any light at all? If light from normal sources, like the sun, or a fire, or incandescent light bulbs is a mix of frequencies, then surely it is a mix a phases as well. If the phase distribution is random, then for every photon of a certain phase, there is just as likely to be a photon of the opposite phase, and they should cancel each other out, so we should see no light at all. Ever.