Conservation of Energy in Double Slit Experiment How is energy conserved In Young's Double Slit Experiment ?
In destructive interference , energy is lost .
So what happens to that lost energy ?  
Does it escape as heat ?
 A: I think your confusion is assuming that the energy of two waves add, when in reality there is an interference term. 
The short, physics-y answer is that it is not that any energy has disappeared, rather the interference has caused some of the energy that 'would have been there' to show up in a different place. The energy got shifted but not destroyed.
This can be backed up with some math. Let's say we have an electromagenetic wave
\begin{equation}
\vec{E}_1(\vec{x},t)=\vec{\mathcal{E}}_1 \cos(\vec{k}\cdot\vec{x} - \omega t)
\end{equation}
where $\vec{\mathcal{E}}_1$ is a constant. Note $B=\frac{1}{c}\vec{k} \times \vec{E}$. I will suppose that I can neglect the magnetic field term in the energy below, to simplify things.
The energy is
\begin{equation}
U_1 = \frac{1}{2}\vec{E}^2 = \vec{E}_1^2 \cos^2(\vec{k}\cdot \vec{x} - \omega t)
\end{equation}
Now let's add a second wave
\begin{equation}
\vec{E}_2(\vec{x},t)=\vec{\mathcal{E}}_2 \cos(\vec{k}\cdot\vec{x} - \omega t+\phi)
\end{equation}
For simplicity let's suppose that the wavenumber and frequency is the same, the only difference is the phase $\phi$.
Now, you might have thought that the energy is $U=U_1+U_2$. However this is not true! The energy is really
\begin{equation}
U=\frac{1}{2}\left(\mathcal{E}_1^2 \cos^2(\vec{k}\cdot\vec{x}-\omega t) + \mathcal{E}_2^2 \cos^2\left(\vec{k}\cdot\vec{x}-\omega t + \phi\right)+2\mathcal{E}_1\mathcal{E}_2 \cos(\vec{k}\cdot \vec{x}-\omega t)\cos(\vec{k}\cdot\vec{x}-\omega t + \phi)\right)
\end{equation}
The last term above is the counterintuitive term that 'shifts the energy around.' 
Finally, to be pedantic I should point out that above I am really talking about the energy density. The true, total energy is the integral of the energy density, and is not sensitive to these kinds of interference effects. In particular, (at least in electromagnetism), the total energy of the two waves is the same as the sum of the energy of each individual wave (the interference term will integrate to zero). Thus interference will shift the energy density around, but will leave the total energy unchanged.
