Published by Patrick Mutisya · 14 days ago
Interference is the phenomenon that occurs when two or more coherent waves overlap in space, resulting in a new wave pattern that is the superposition of the individual waves.
For two waves of equal amplitude \$A\$, the resultant intensity \$I\$ at a point is given by
\$I = 4I_0\cos^2\!\left(\frac{\Delta\phi}{2}\right)\$
where \$I_0\$ is the intensity of each individual wave and \$\Delta\phi\$ is the phase difference between them.
The type of interference depends on the path difference \$\Delta r\$ between the waves:
Coherence describes the ability of two waves to produce a stable interference pattern. It quantifies how well the phase relationship between the waves is maintained over time and space.
The coherence time \$\tau_c\$ is the time over which the phase remains predictable and is given by
\$\tau_c \approx \frac{1}{\Delta\nu}\$
where \$\Delta\nu\$ is the spectral width of the source. The corresponding coherence length \$L_c\$ is
\$Lc = c\,\tauc = \frac{c}{\Delta\nu}\$
For a perfectly monochromatic source (\$\Delta\nu \to 0\$), \$\tauc\$ and \$Lc\$ become infinite, allowing interference over arbitrarily large path differences.
| Aspect | Temporal Coherence | Spatial Coherence |
|---|---|---|
| Definition | Correlation of phase at different times for the same point | Correlation of phase at different points across a wavefront |
| Key Parameter | Coherence time \$\tauc\$ (or length \$Lc\$) | Coherence area (or source size) |
| Effect on Interference | Limits maximum path difference that still yields visible fringes | Determines angular spread over which fringes remain sharp |
| Typical Sources | Lasers (large \$\tau_c\$), narrow‑band LEDs | Point sources, small apertures |
In experiments such as the double‑slit or Michelson interferometer, achieving sufficient coherence is essential. If the path difference exceeds \$L_c\$, the interference fringes wash out because the waves are no longer phase‑related.