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AP Physics 2
14.9 Thin-Film Interference
AdvancedMCQMathematicalProportional AnalysisConceptual20.6k
Two side-by-side cross-sectional diagrams labeled Configuration X on the left and Configuration Y on the right. In Configuration X, three horizontal layers are shown from top to bottom: Air with label n_air = 1.0, Film 1 with thickness t_X and refractive index n_1, and Substrate with refractive index n_2, accompanied by text n_1 > n_2 > 1.0. A downward vertical arrow representing incident light of wavelength \lambda_0 enters Film 1, with two upward vertical arrows representing reflected rays from the top boundary and bottom boundary of Film 1. In Configuration Y, the same three-layer geometry is shown with Film 1 of thickness t_Y and text 1.0 < n_1 < n_2. No other labels, lines, text, or axes appear.
Thin-film reflection setups for Configuration X and Configuration Y.
A thin film of refractive index \(n_1\) is deposited on a thick substrate of refractive index \(n_2\). Monochromatic laser light of wavelength \(\lambda_0\) in air (\(n_{\text{air}} = 1.0\)) is normally incident on the film. In Configuration X, the refractive indices satisfy \(n_1 > n_2 > 1.0\), while in Configuration Y, they satisfy \(1.0 < n_1 < n_2\). If \(t_{\text{X}}\) and \(t_{\text{Y}}\) are the minimum non-zero film thicknesses required for maximum constructive interference of the reflected light in Configurations X and Y, respectively, what is the ratio \(\dfrac{t_{\text{X}}}{t_{\text{Y}}}\)?

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