Q: What would happen if white light were used in the double slit experiment?
Understanding the Basics:
In the traditional Young’s double-slit experiment, interference patterns are observed using monochromatic light (light of a single wavelength). This produces sharp, well-defined bright and dark fringes due to constructive and destructive interference.
However, if the monochromatic light is replaced with white light, which contains a continuous spectrum of wavelengths, the observed pattern becomes significantly more complex.
🔍 Key Observations When Using White Light:
- 1. Coherence Issues:
White light has a very short coherence length because it contains multiple wavelengths. Interference requires a fixed phase relationship between waves, which is hard to maintain across a broad spectrum.
As a result, clear interference fringes appear only near the central region (zero-order fringe) unless special coherence-enhancing arrangements are used (like spatial filtering).
- 2. Fringe Dispersion:
For monochromatic light, the condition for constructive interference is given by:
d sin θ = mλ
Here, d is slit separation, θ is the fringe angle, m is the order, and λ is the wavelength. With white light, each wavelength satisfies this condition at a different angle. So, red light (longer λ) shifts further out, while blue (shorter λ) appears closer.
- 3. Colored Fringes:
Instead of uniform bright fringes, you get rainbow-like fringes. This is because each color interferes constructively at slightly different positions, leading to a dispersion effect.
The central fringe appears white (all colors constructively interfere at θ = 0), while higher-order fringes split into colored bands.
- 4. Limited Visibility:
Due to short coherence length, the interference pattern is confined to a narrow region around the central fringe. Beyond this, the path difference becomes too large, and fringe visibility diminishes quickly.
✅ Summary:
- A bright white central fringe is observed where all wavelengths overlap constructively.
- Higher-order fringes appear as colored (rainbow-like) bands.
- Fringes are only visible in a narrow central region due to limited coherence.
This fascinating phenomenon illustrates how interference depends critically on both wavelength and coherence. For precise white-light interference, special arrangements such as narrow slits, pinholes, or filters are often required.