Thin-film interference

Two reflected waves meet: one off the front face of the film, one that crossed the film, reflected off the back face, and came out again. Whether they add or cancel depends on two things, and the order matters.

First count the phase flips, because that is where the errors live. The CED gives the rule as two statements: a reflection off a medium of greater index than the one the light is in flips the wave by 180 degrees, and a reflection off a medium of lower index does not. Refraction never changes the phase.

• Zero flips or two flips: constructive when $2t = m\lambda_{\text{film}}$.
• Exactly one flip: the conditions swap, and constructive becomes $2t = \left(m + \tfrac{1}{2}\right)\lambda_{\text{film}}$.

Then use the wavelength inside the film, not in air. The extra path is travelled in the film, so $\lambda_{\text{film}} = \lambda_0 / n$, where $n$ is the film's index of refraction. Substituting $\lambda_0$ is the second standard error.

A soap bubble in air flips once, at the top surface only, so its thinnest region reflects almost nothing and looks black just before it bursts. An antireflection coating is built the other way: the CED says the simplest one is a quarter of a wavelength thick in the coating, with an index above air and below the surface it covers, so both reflections flip and the quarter-wave path cancels them.

The CED's boundary statement limits quantitative work to light normal to the incident surface, with no exception clause, and no thin-film equation is printed on the sheet.