1. What interference means
Interference happens when two light waves overlap and combine. Because waves add according to the superposition principle, the result can be:
- a brighter region when they add up, or
- a darker region when they cancel out.
This creates a pattern of bright and dark fringes.
2. Why interference occurs only for waves
For interference to happen, the disturbances must overlap in space and time. Light can do this because it is a wave. When the electric fields of two waves add, they produce a new resultant wave.
This behaviour cannot be explained with simple rays — it needs the wave picture.
3. Conditions for sustained interference
To get a stable pattern of bright and dark fringes, the two light waves must satisfy two important conditions:
3.1. Coherent sources
The two waves must have a constant phase difference. This happens only when they come from the same source or behave as if they do.
Two independent bulbs do not produce interference because their phases vary randomly.
3.2. Same frequency (or wavelength)
The colours must match. If the wavelengths differ, the pattern shifts and rapidly becomes unstable.
4. Constructive and destructive interference
The resulting intensity at a point depends on how the peaks and troughs of the waves line up.
4.1. Constructive interference
When crests meet crests or troughs meet troughs, the waves add. The phase difference is:
\( \Delta \phi = 2n\pi \; (n = 0, 1, 2, ...) \)
This gives bright fringes.
4.2. Destructive interference
When a crest meets a trough, the waves cancel. The phase difference is:
\( \Delta \phi = (2n + 1)\pi \)
This gives dark fringes.
5. Path difference and fringe formation
Instead of thinking in terms of phase difference, I often use path difference — the difference in distances the two waves travel before meeting.
The rules become:
5.1. For constructive interference
\( \Delta x = n\lambda \)
(waves add)
5.2. For destructive interference
\( \Delta x = (2n + 1)\dfrac{\lambda}{2} \)
(waves cancel)
6. Young’s Double Slit Experiment (YDSE): the classic example
Two coherent sources are created using a single light source and two narrow slits placed very close to each other. The waves from these slits overlap on a screen and form a pattern of alternating bright and dark bands called fringes.
6.1. Fringe width
The distance between two consecutive bright (or dark) fringes is called fringe width. It is given by:
\( \beta = \dfrac{\lambda D}{d} \)
where:
- \(\lambda\) = wavelength of light
- \(D\) = distance between slits and screen
- \(d\) = separation between the slits
7. Why fringes are equally spaced
Because the two slits are very close and behave like identical sources, the path difference changes linearly along the screen. That is why the bright and dark fringes appear evenly spaced.
8. Interference in daily life
I notice interference patterns in many places:
- Colours in soap bubbles and thin oil films
- Spectral colours on a CD surface
- Multiple reflections in glass surfaces
- Anti-reflection coatings on lenses
All of these occur because light waves overlap and combine according to the superposition principle.
9. Why interference proves the wave nature of light
If light were only particles or rays, we would never see alternating bright and dark regions. The existence of stable interference fringes is one of the strongest evidences that light behaves like a wave.