What in the world is constructive and destructive interference?

When two light waves intersect and thus interact with each other, interference occurs. Using water waves as an analogy, two crests (high points on the waves) or two troughs (low points) at the same place constructively interfere, adding together to produce a higher crest and a lower trough. Where a crest of one wave, however, meets a trough of another wave, there is a mutual cancellation or destructive interference. Natural interference occurs in oil slicks, producing colored patterns as the constructive interference of one wavelength occurs where other wavelengths destructively interfere.

Astronomers make use of interference as another means of dispersing white light into its component colors. A transmission grating, consisting of many slits (like a picket fence, but numbering in the thousands per centimeter of distance across the grating), produces constructive interference of the various colors as a function of angle. A reflection grating using multiple reflecting surfaces can do the same thing with the advantage that all light can be used and most of light energy can be thrown into a specific constructive interference region. Because of this higher efficiency, all modern astronomical spectrographs use reflection gratings.