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AP Physics 2
14.9 Thin-Film Interference
AdvancedMCQMathematical20.2k
A diagram showing three horizontal layers representing optical media. The top layer is labeled n_1. Below it is a middle layer of uniform vertical thickness t, labeled n_2. Below the middle layer is a thick bottom layer labeled n_3, with the inequality n_1 < n_2 < n_3 indicated. A single ray of light with wavelength \lambda_0 enters from the top layer n_1, moving downward perpendicular to the top interface between n_1 and n_2. At the top interface, a reflected ray arrow points back upward into n_1. A transmitted ray arrow continues downward through the layer n_2 of thickness t, hits the lower interface between n_2 and n_3, and reflects upward, passing back out through n_1. No other labels, lines, text, or axes appear.
Light incident on a thin film of index $n_2$ on a substrate of index $n_3$.
A thin protective coating with index of refraction \(n_2\) and uniform thickness \(t\) is applied to the surface of a glass lens with index of refraction \(n_3\). The coated lens is surrounded by air with index of refraction \(n_1\), where \(n_1 < n_2 < n_3\). Monochromatic light of vacuum wavelength \(\lambda_0\) travels through air and falls perpendicularly onto the coating. Which of the following expressions represents the minimum non-zero coating thickness \(t\) that results in maximum constructive interference of the reflected light?

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