Superposition of Lights

If the component waves of a beam of light of a single frequency have a fixed phase relationship with each other, the light is coherent (e.g., the laser). Two beams of light are coherent if the phase difference between their waves is constant. For example, two beams produced by splitting a single laser beam are coherent and they form stable interference patterns when combined. On the other hand, a light is non-coherent if its component waves have a random or changing phase relationship, such as light produced by an incandescent light bulb.

The intensities of incoherent lights add linearly, i.e., the spectral energy distribution of the mixture of two lights is the linear combination of their individual energy distributions. In other words, the spectral energy distribution of the mixture of a set of $n$ lights with intensities $c_i,\;\;(i=1,\cdots, n)$ is the weighted sum of their individual spectral distributions $L_i(\lambda),\;\;\;(i=1,\cdots,n)$:

$$L_{mixture}(\lambda)=\sum_{i=1}^n c_i L_i(\lambda)$$