Young's double-slit interference
The formula β = λD/d is easy to write down and hard to picture — what actually happens on the screen when two coherent waves overlap? So build the two-slit setup and watch. Drag the wavelength, slit separation or screen distance and the fringe pattern redraws live, straight from the interference equations.
The physics you're seeing
Coherent sources
The two slits act as two coherent sources — same frequency, constant phase relationship. That's why a stable pattern is even possible: two separate bulbs would never produce visible fringes.
Constructive interference
Bright fringes occur where the path difference from the two slits is a whole number of wavelengths: Δ = nλ (n = 0, ±1, ±2, …).
Destructive interference
Dark fringes occur where the path difference is a half-integer number of wavelengths: Δ = (n+½)λ.
Fringe width
β = λD/d. Fringes get wider with a longer wavelength or a farther screen, and narrower with wider slit separation.
Part of the Wave Optics chapter — read the notes, grab the formula sheet and take the quiz. One of Priodemy for School, free with every EduSuite school.
What the fringe pattern is telling you
Why two slits and not one
The experiment works because the two slits are cut from a single wavefront, which makes them coherent — they keep a constant phase relationship. Two separate bulbs, however identical, would not: their phase difference drifts randomly millions of times a second, the pattern washes out, and you see uniform illumination. This is the reason Young's original setup used one source and split it, and it is why the question "why can't we use two lamps" appears so often in exams.
At any point on the screen the two waves have travelled slightly different distances. That path difference decides everything. Where it equals a whole number of wavelengths, the crests line up, the waves reinforce, and you get a bright fringe: the condition is path difference = nλ. Where it equals an odd number of half-wavelengths, a crest meets a trough and they cancel, giving a dark fringe at (n + ½)λ.
Reading the formula off the screen
The spacing between consecutive bright fringes is the fringe width, β = λD/d, where λ is the wavelength, D the slit-to-screen distance and d the separation between the slits. Every symbol in that formula is a slider here, so you can test each one independently instead of trusting the algebra.
Increase the wavelength — drag from blue towards red — and the fringes spread out, because β is proportional to λ. Push the screen further away and they spread too, for the same reason. Now increase the slit separation d and the pattern contracts, because d is in the denominator. That inverse relationship is the one students most often get backwards, and it is worth seeing happen: bringing the slits closer together makes the pattern wider, not narrower.
What to try
- Set the wavelength to roughly 400 nm and then 700 nm, and compare fringe widths. Red light produces noticeably wider fringes than violet — the physical basis of the coloured fringes you see in white light.
- Make d very large and watch the fringes crowd together until they are no longer resolvable. This is why the slits must be close for the effect to be visible at all.
- Count outwards from the centre and check that the nth bright fringe sits at a distance nβ from the middle.
Mistakes that cost marks
Mixing up d and D. They differ by one capital letter and by about six orders of magnitude — d is a fraction of a millimetre, D is around a metre. Substituting them the wrong way round gives an answer that is wrong by an enormous factor, so a quick sanity check on the size of your fringe width will catch it.
Forgetting to convert units. Wavelengths are quoted in nanometres, slit separations in millimetres, screen distances in metres. The formula needs all three in the same unit, and marks are routinely lost to a stray factor of 1000 rather than to any misunderstanding of the physics.
Confusing interference with diffraction. Both produce bright and dark bands. Interference from two slits gives fringes of roughly equal brightness and equal spacing; single-slit diffraction gives a wide, dominant central maximum with much fainter side maxima. A question that mentions one slit is not asking about β = λD/d.