What you are looking at
White light strikes a film a few hundred nanometres thick. Part reflects off the top surface; part dives in,
reflects off the bottom, and comes back out. Those two gold rays overlap and interfere — the swatch shows
the net reflected colour, and the graph shows the reflectance across the whole visible spectrum.
The race between two reflections
The inner ray travels an extra optical path of
Δ = 2·n·t·cosθₜ
(thickness both ways, at the refracted angle, and slowed by the index n). Whether the two rays reinforce or
cancel depends on this Δ against the wavelength —
plus one subtlety: reflecting off a
higher-index medium flips the wave's phase by half a cycle (π); reflecting off a lower one
doesn't.
Soap film vs lens coating: opposite rules
A
soap film in air flips only the top reflection, so the two rays start half a cycle apart:
dark (reflection cancelled): 2nt·cosθₜ = mλ · bright: 2nt·cosθₜ = (m−½)λ
A
coating on glass (n_film < n_glass) flips both reflections, so the flips cancel and
the rules swap:
bright: 2nt·cosθₜ = mλ · dark: 2nt·cosθₜ = (m−½)λ
Same physics, opposite outcomes — the toggle above lets you see both.
Two famous consequences
The black film: drag the soap film's thickness toward zero and Δ vanishes — but the π flip
remains, so every colour cancels and the film reflects nothing. Real bubbles turn black at the top moments
before popping.
The anti-reflective coating: in coating mode, set t = λ/4n. The two
reflections then arrive exactly half a wavelength apart and erase each other at that colour — this is the
purple-green sheen on camera lenses and glasses, killing reflections where the eye is most sensitive.
Why bubbles swirl with colour
A real bubble's wall varies in thickness from place to place (and drains downward under gravity), so each
patch cancels a different wavelength and reflects a different colour. Tilting also changes cosθₜ — the same
patch shifts colour as you move your head. Oil slicks on wet roads are the same physics on water.
Things to try
Slide t slowly from 900 nm down to 5 nm and watch the spectrum's peaks spread apart, simplify, and finally
all sink to zero — the black film. Switch to coating mode and dial t to the quarter-wave value shown in the
stats: the 550 nm reflectance drops to zero. Then increase the angle and watch every feature slide blueward
as cosθₜ shrinks the optical path.