When two beams make darkness
The ray model says: add more light, get more brightness. Yet in 1801 Thomas Young shone light through two narrow slits and found the screen striped with bright and dark bands — places where light plus light gave darkness. Rays cannot do this; waves can. Where two waves arrive crest-on-crest they reinforce (bright); crest-on-trough they cancel (dark). This adding-up is the superposition principle, and the pattern it makes is interference.
The key quantity is the path difference: how much farther one wave travelled than the other to reach a given point. If that extra distance is a whole number of wavelengths, the waves arrive in step — constructive interference, a bright fringe. If it is a half-integer number of wavelengths, they arrive exactly out of step — destructive interference, a dark fringe.
Young's double slit
Two slits a distance d apart, lit by a single colour (monochromatic light of wavelength \lambda), act as two synchronized wave sources. On a screen a distance L away, the path difference to a point at angle \theta from the centre is d\sin\theta. Set that equal to a whole number of wavelengths and you get the bright fringes of double-slit interference.
Bright fringes of the double slit. m is the order; m = 0 is the central bright fringe straight ahead. Dark fringes sit at half-integer m.
For the small angles usual in a lab, \sin\theta \approx \tan\theta = y/L, which gives an evenly spaced ladder of fringes. The spacing \Delta y between neighbouring bright bands is a clean, measurable result — and it let Young measure the wavelength of light with a ruler, long before anyone knew what light was made of.
Fringe spacing on the screen (small-angle approximation). Wider slit separation d packs the fringes closer; longer wavelength spreads them out.
Diffraction: light bends around edges
Why do the slits act as sources at all? Because each opening makes light spread as it passes through — diffraction. Every point of a wavefront re-radiates a little wavelet (Huygens' idea), and their sum bends light into the geometric shadow. Diffraction is why you cannot make a perfectly sharp shadow, why a distant streetlight flares through a curtain, and why even a single narrow slit throws a pattern of its own: a bright central band flanked by weaker fringes, with dark minima where a\sin\theta = m\lambda (here a is the slit width, and m \neq 0).
Dark minima of single-slit diffraction. Note m = 0 is excluded — the centre is a bright maximum. Narrower slits (small a) spread light more, the opposite of intuition.
Gratings and thin films
Push the idea further. Rule not two slits but thousands, evenly spaced, and you have a diffraction grating. The same condition d\sin\theta = m\lambda holds, but with thousands of beams adding, the bright fringes become razor-sharp and each wavelength lands at its own precise angle. A grating splits light into a pure spectrum far better than a prism — it is the heart of the spectrometers that read the chemistry of distant stars, and the shimmer on a CD.
Finally, the colours in a soap bubble or an oil slick come from thin-film interference. Light reflects off both the top and bottom surfaces of a very thin film; the two reflections travel slightly different distances and interfere. Because the condition depends on wavelength, some colours reinforce and others cancel at each thickness, painting the film with shifting iridescence. Engineers run the trick in reverse: an anti-reflection coating on a camera lens is a film tuned so reflected light cancels, sending more light through.
A representative thin-film condition: constructive reflection for a film of index n and thickness t in air, including the half-wavelength shift on reflecting off a denser medium. The extra ½ is easy to forget — and it flips bright and dark.