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AP Physics 2
14.9 Thin-Film Interference
AdvancedMCQMathematical22.6k
A cross-sectional diagram of a wedge-shaped thin film on a substrate. At the bottom, a thick horizontal rectangular block is labeled 'Silicon substrate (n_s)'. On top of the substrate, a thin right-triangular wedge layer is labeled 'Silicon dioxide film (n_f)', tapering down to zero thickness at x = 0 on the left and thickening toward the right. The medium above the wedge is labeled 'Air (n_0 = 1)'. A horizontal axis labeled x extends to the right along the substrate interface, with origin x = 0 at the left tip of the wedge. Parallel downward vertical arrows labeled 'Monochromatic light (\lambda)' strike the upper surface of the film from above. No other labels, lines, text, or axes appear.
Cross section of a wedge-shaped silicon dioxide film on a silicon substrate.
A silicon wafer is coated with a wedge-shaped layer of silicon dioxide (index of refraction \(n_f\)) resting on a silicon substrate (index of refraction \(n_s\)). The indices of refraction satisfy \(1 < n_f < n_s\). The film thickness increases linearly with horizontal position \(x\) according to \(t(x) = C x\), where \(C\) is a positive constant and \(x = 0\) corresponds to the edge of the film. Monochromatic light of wavelength \(\lambda\) in air strikes the film at normal incidence. Which of the following expressions represents the distance \(x_1\) from the edge (\(x = 0\)) to the first bright fringe observed at a position \(x > 0\) in reflection?

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