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Two slits act as coherent sources, producing a characteristic pattern of vertical bright and dark fringes on a distant screen. The fringe spacing is λD/d, where D is the distance to the screen and d is the slit separation. This experiment demonstrates the wave nature of light and provides a method to measure wavelength.
Derive the positions of bright fringes using path difference geometry and the condition for constructive interference.
The double slit does not create the interference pattern—the two coherent waves created by diffraction at each slit interfere to form the pattern.
You already know the conditions for bright and dark fringes: constructive interference occurs when two waves arrive in phase (path difference = nλ), and destructive interference when they arrive out of phase (path difference = (n + ½)λ). Young's double-slit experiment is the classic setup that makes these conditions physically visible as a repeating pattern of light and dark stripes on a distant screen — and it is worth understanding the geometry that produces the formula, not just memorizing the formula itself.
Here is the setup: two narrow, closely spaced slits are illuminated by coherent light (light with a stable phase relationship, so the waves from each slit stay synchronized). Each slit acts as a new source of spreading waves through diffraction. These two coherent wave fronts overlap in the space beyond the slits. At any point on a distant screen, waves from the two slits have traveled slightly different distances. That path difference determines whether they arrive in phase or out of phase. Along the central axis — directly in front of the midpoint between the slits — the path difference is zero, giving perfect constructive interference and the central bright fringe. Moving up or down from center, the path difference grows. The first bright fringe (order m = 1) appears where path difference equals exactly one wavelength (λ); the first dark fringe appears where it equals half a wavelength (λ/2).
This geometry produces a regular, symmetric ladder of bright and dark bands with a constant spacing. The fringe spacing formula Δy = λD/d connects the measurable geometry (screen distance D, slit separation d) to the wavelength λ. Shorter-wavelength (bluer) light produces more tightly packed fringes; longer-wavelength (redder) light produces more widely spaced fringes. By measuring the fringe spacing and the geometry, you can solve for λ — which is how wavelength was measured precisely long before modern instruments existed.
The deepest lesson is historical and conceptual: at the start of the 19th century, this experiment settled the wave-versus-particle debate in favor of the wave model of light. Particles don't interfere — if you shot bullets through two slits, you'd get two stripes on the wall behind them, not a multi-stripe pattern. The fact that light creates many alternating bright and dark fringes is direct evidence of its wave nature. When you observe a double-slit pattern, you are watching wavelengths add and cancel across space, made visible as light and shadow.