What happens if we prepare superposition of two monochrome sinusoidal beams of light which are exactly the same but have $\pi$ differences in their phases? getting nothing?!
$$E_1+E_2 = A\cos(kx-\omega t) + A\cos(kx-\omega t+\pi) =0 \quad\quad\quad!! $$
This is how perfect reflection can be interpreted. The electrons at its surface of a perfect mirror respond by emitting two waves wave that are out of phase by $\pi$. One is the well known reflected wave. The other travels with the incoming wave and exactly cancels the incoming wave beyond the reflective surface, exactly as in your example.
The superposition principle and the conservation of energy always hold, even when waves cancel each other. At first glance, destructive interference might seem to contradict energy conservation. The resolution is that the field amplitude and the power consumed by the sources are not independent. The radiated field amplitude is determined by the balance between the input power and the system’s energy losses.
If the sources are exactly out of phase, the radiated fields cancel in the overlap region. In this case, the sources deliver much less power to the radiation field and therefore consume less power overall. If the input power is held constant and there is nowhere for the excess energy to go, perfect cancellation cannot be sustained. The field amplitude will adjust until the rate of energy loss (through radiation, absorption, or dissipation) equals the supplied power.
When the waves are in phase, their amplitudes add, and the resulting intensity is four times that of a single source. To sustain such a strong field, the sources must each draw more power. If the input power remains fixed, the combined amplitude cannot be sustained.
Thus, interference does not destroy energy. Constructive interference requires the sources to consume more power, destructive interference reduces the net power delivered to the field, and if the power supply is held constant, the field amplitude adjusts until energy conservation is satisfied.
To be fair one needs to provide a complete description of the experimental setup with which one intends to demonstrate such a cancellation. It turns out that it is almost impossible to do it in free space, because optical beams are finite and when they propagate they pick up some phase curvature. So, by trying to produce such a cancellation with a beamsplitter for example, one would need to match the two beam shapes from the different sources exactly.
It is easier to do it in single-mode optical fibre because the transverse mode is fixed and the only variables are the amplitude and the phase. In this case, the beamsplitter is replaced by a fibre coupler. Like the beamsplitter, it is a four-port device with two input ports and two output ports. To demonstrate the cancellation, one needs to tune the phases of the two incoming fields to be exactly out of phase when they exit one of the two output ports. Well in that case, they'll be exactly in phase for the other exit port. So all the light will leave through the other exit port. Energy is conserved.
