Two Slits Draw Fringes on a Screen
When light passes through two narrow slits, a regular pattern of bright and dark stripes appears on a screen. The waves leaving the two slits meet, and where crest lines up with crest the screen brightens, while crest meeting trough leaves it dark. A bright stripe sits wherever the two path lengths differ by a whole number of wavelengths, d sinθ = mλ, and the on-screen spacing is Δy = λL/d. This lesson takes the classical view of light as a continuous wave. For how single photons, one at a time, still build up the very same pattern, see the qm-wave-particle lesson in the quantum-mechanics area.
Widen the gap d between the slits and the stripes crowd together. Because the spacing is Δy = λL/d, a larger d means a larger denominator and a smaller spacing. Visible light has such a short wavelength that, to spread the fringes wide enough to see, the slit spacing d has to be made smaller than a millimeter. Slide d up and watch the bright bands on the screen move closer together as the value of Δy shrinks with them.
Now change the wavelength λ. Since λ sits in the numerator of λL/d, a longer wavelength gives wider spacing. Red light spreads its fringes far apart while blue light packs them tight. With white light the central stripe looks white because every color overlaps at the same spot, while the side stripes fan out like a rainbow since each color lands in a different place. Slide the color across and see how the same apparatus produces different fringe widths for different wavelengths.
Move the screen farther away, increasing L, and the whole pattern grows. In Δy = λL/d the distance L is in the numerator, so the stripe spacing widens in proportion to it. The angles stay the same; the same angle simply spans a larger gap the farther it travels. However, increasing L widens the pattern but also dims it, since the same light is spread over a larger area. Slide L up and watch the pattern magnify.
Drag the probe up and down along the screen. At each position it computes the path-length difference d sinθ between the two slits. When this difference equals a whole number of wavelengths mλ, that spot is a bright stripe; a half-integer leaves it dark. Where the path difference is off by a half wavelength, (m+½)λ, the crest of one wave overlaps the trough of the other and cancels, leaving a dark stripe. Move the probe to find where the order m turns to 0, 1, 2 and check that those spots land on the bright bands.
Switch to a single slit and you are left with one broad, smooth hump of brightness. That is the diffraction pattern a single wide slit makes on its own. Switch back to two slits and the inside of that hump is carved into fine interference stripes. In other words, the two-slit fringes dance inside an envelope set by one slit. The narrower each single slit is, the wider its diffraction hump spreads, so more interference stripes fit inside it. This envelope story continues in the next lesson on diffraction.