To understand the conditions required for the observation of interference fringes produced by two coherent sources.
The two waves must have the same wavelength $\lambda$ (or a very narrow range of wavelengths).
The phase difference $\Delta\phi$ between the sources must remain constant in time.
Both waves should be polarised in the same direction; orthogonal polarisations do not interfere.
The effective size of each source must be much smaller than the fringe spacing, otherwise fringe contrast is reduced.
Constructive interference occurs when the path difference $\Delta r$ satisfies $$\Delta r = m\lambda \quad (m = 0, \pm1, \pm2,\dots)$$ and destructive interference when $$\Delta r = \left(m+\tfrac12\right)\lambda.$$
The relative positions of the sources and the observation screen must remain fixed during the measurement.
The distance over which the wave maintains a well‑defined phase (coherence length $L_c$) must exceed the maximum path difference in the experiment.
For the classic double‑slit geometry, the fringe spacing $ \beta $ on a screen a distance $D$ from the slits (separation $d$) is given by
$$\beta = \frac{\lambda D}{d}$$where $d \ll D$ so that the small‑angle approximation holds.
| Condition | Requirement | Consequence if Not Satisfied |
|---|---|---|
| Same frequency | Monochromatic light (single $\lambda$) | Fringe washing out due to varying $\lambda$ |
| Constant phase | Coherent sources (fixed $\Delta\phi$) | Temporal variation → blurred fringes |
| Identical polarisation | Same polarisation direction | No interference if orthogonal |
| Small source size | Angular size $\ll$ fringe angular spacing | Reduced visibility (contrast) |
| Path‑difference $\sim\lambda$ | $\Delta r$ within a few $\lambda$ | Only intensity variations, no distinct fringes |
| Stable geometry | Fixed $d$, $D$, and alignment | Moving fringes, measurement error |
| Coherence length $L_c$ | $L_c \gg$ maximum $\Delta r$ | Fringe contrast falls off with distance |