Interference

Two waves interfere $\text{constructively}$ (a bright fringe / loud sound) when they arrive $\text{in phase}$. This happens when their $\text{path difference}$ — the extra distance one has travelled — is a whole number of wavelengths. They interfere $\text{destructively}$ (dark / quiet) when they arrive in antiphase, at a path difference of an odd number of half-wavelengths.

For the pattern to hold still rather than flicker, the sources must be $\text{coherent}$: same frequency and a $\text{constant phase difference}$. Lasers are naturally coherent, which is why they are ideal for interference experiments.

Monochromatic light passes through two narrow slits a small distance $s$ apart. The slits act as two coherent sources (they are lit by the same wave), and the light spreading from them overlaps on a screen a distance $D$ away, producing a pattern of evenly spaced bright and dark $\text{fringes}$.

Each bright fringe marks a point where the path difference from the two slits is a whole number of wavelengths; each dark fringe a half-integer number. Using a single source and a single slit before the double slit guarantees the light reaching both slits is coherent.

The spacing $w$ between adjacent bright (or adjacent dark) fringes is given by the fringe equation. Because $w$ is directly proportional to wavelength, measuring $w$, $s$ and $D$ lets you calculate the wavelength of the light.

Wider fringes (easier to measure) come from a longer wavelength, a bigger slit-to-screen distance $D$, or a smaller slit separation $s$.

With $\text{monochromatic}$ (single-wavelength) light the fringes are sharp and equally bright. With $\text{white light}$ each colour has its own fringe spacing, so you get a bright $\text{white central fringe}$ (where all colours have zero path difference) flanked by fringes with coloured edges — blue nearest the centre, red furthest, since red has the longer wavelength.

Lasers are used because they are coherent and monochromatic, but they are intense: never look into the beam or its reflection, wear laser-safety goggles, and display a warning sign.