Thin-Film Constructive Interference (Bright Reflection)

Light reflecting off the top of a soap film and light reflecting off its bottom travel paths that differ by 2nt — twice the thickness, counted in the film's own slower wavelength λ/n. That alone would make 2nt = mλ the bright condition. But the top reflection happens at a jump into a denser medium and flips the wave by half a cycle, while the bottom reflection, going back out into air, does not. One inversion, one extra half-wave, and the two conditions swap places: bright reflection needs 2nt = (m + ½)λ.

Newton measured this beautifully and explained it wrongly. Pressing a lens onto a flat plate gives an air film that thickens with radius, and the concentric coloured rings that appear — Newton's rings — are this equation drawn on glass. He published careful measurements in Opticks (1704) and even extracted what we would call a wavelength, then forced them into his corpuscular theory with "fits of easy reflection and easy transmission", a periodic disposition he attached to the particles themselves. He resisted waves because waves, in his mind, had to bend round corners the way sound does, and light plainly cast sharp shadows. It took Thomas Young a century later to point at Newton's own rings and say: this is interference.

Worked case: a soap film with n = 1.33 and t = 100 nm reflects brightest at λ = 2(1.33)(100 nm)/0.5 = 532 nm — green. Let the film drain and thin toward nothing and 2nt → 0, which no longer satisfies any bright order; the top of a draining bubble goes black just before it bursts, the clearest visual proof that the half-wave flip is real.