Young's double-slit experiment
Send light through two narrow openings and a regular pattern of bright and dark stripes appears on the screen. Waves from the two openings meet, and the stripe is bright where crest meets crest and dark where crest meets trough. A bright stripe happens when the difference in path length is a whole number of wavelengths, that is d sinθ = mλ, and the spacing of the stripes on the screen is fixed by Δy = λL/d. This lesson takes the classical view of light as a continuous wave. How single photons pile up into this pattern is taken up in the quantum-mechanics lesson qm-wave-particle. Those two lines of formula hold the whole spacing.
Widen the gap d between the slits and the stripes pack tighter. The spacing is Δy = λL/d, so a larger gap makes a larger denominator. Visible light has a very short wavelength, so to spread the stripes far enough to see, the gap between the slits has to be smaller than a millimeter. Raise the gap and the bright bands on the screen move closer together, and the spacing shrinks with them. The wider the gap, the closer the stripes.
Now change the wavelength. The wavelength sits in the numerator of the spacing, so a longer wavelength makes a wider spacing. Red light therefore spreads its stripes wide, and blue light gathers them tight. With light of many colors the center stripe looks white, because every color lands in the same place, while the stripes to either side spread into a rainbow, because each color sits somewhere else. Change the color and, on the same apparatus, the width of the pattern changes with the wavelength. A long wavelength makes a wide stripe.
Increase the distance between the slits and the screen and the whole pattern grows. In Δy = λL/d the distance sits in the numerator, so a greater distance spreads the spacing in proportion. The angle stays the same, yet farther away the same angle opens into a larger gap. Stretch the distance, though, and the pattern grows wider while the same light spreads over a larger area, so it grows dimmer by that much. Increase the distance and the pattern enlarges. It grows dim as it grows wide.
Move the probe up and down the screen and the difference in path length from the two slits, d sinθ, is computed at each place. When that difference matches a whole number of wavelengths the place is a bright stripe, and when it matches a half-integer it is a dark stripe. At a place off by half a wavelength, (m+½)λ, the crest of one wave meets the trough of the other and they cancel, so the stripe is dark. Move the probe to the places where the order m becomes 0, 1, 2 and you can check that they land on the bright bands. The order points to the place of the stripe.
Switch to a single slit and only one broad, soft peak of brightness remains. That is the diffraction pattern made by one wide opening. Switch back to two openings and the inside of that peak breaks into fine interference stripes. The two-opening pattern dances inside the envelope made by one opening. The narrower the single opening, the wider the diffraction peak spreads, and the more interference stripes it holds. This story of the envelope continues into the next lesson, diffraction. The width of one opening decides the house of the many stripes.