Light waves can superpose just like other waves. When coherent light reaches the same region by different paths, the phase difference can produce bright and dark interference fringes.

Two-source interference

For two coherent sources with wavelength $\lambda$, constructive interference occurs when the path difference satisfies

$$\Delta L=m\lambda,$$

while destructive interference occurs when

$$\Delta L=\left(m+\frac12\right)\lambda.$$

Double-slit pattern

Two narrow slits illuminated coherently act as two wave sources. On a distant screen, alternating regions of constructive and destructive interference appear.

For small angles, the bright-fringe spacing is approximately

$$\Delta y=\frac{\lambda L}{d},$$

where $L$ is the screen distance and $d$ the slit separation.

Coherence

A stable fringe pattern requires a stable phase relationship. Ordinary independent light sources generally do not maintain such coherence, so their rapidly changing interference averages out.

Wave evidence

Ray optics alone does not predict alternating bright and dark regions from overlapping paths. Interference therefore reveals the wave character of light directly.