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AP Physics 2
13.3 Refraction
AdvancedMCQMathematical25.3k
A schematic cross-sectional diagram showing two horizontal parallel slabs stacked vertically in air. The top slab has thickness d_1 and refractive index n_1. The bottom slab has thickness d_2 and refractive index n_2. A single light ray approaches from the top left in air at an angle theta_0 relative to the vertical normal. The ray refracts at the top surface into slab 1 at a smaller angle, refracts again at the interface into slab 2, and emerges from the bottom surface of slab 2 back into air at angle theta_0 parallel to its initial path. A dashed line extends the original incident ray's trajectory straight through both slabs to illustrate the un-refracted path. Double-headed arrows indicate thicknesses d_1 and d_2 on the left side, and a horizontal double-headed arrow labeled Delta x indicates the lateral displacement between the dashed un-refracted line and the emerging ray at the bottom interface. No other labels, lines, text, or axes appear.
A light ray refracting through two parallel stacked slabs.
A light ray traveling in air with refractive index \(n_0 = 1\) is incident at a small angle \(\theta_0\) relative to the normal onto two stacked, parallel transparent slabs. The top slab has thickness \(d_1\) and index of refraction \(n_1\), and the bottom slab has thickness \(d_2\) and index of refraction \(n_2\). After passing through both slabs, the ray emerges back into air parallel to its original path but shifted laterally by a distance \(\Delta x\). Which of the following expressions is a correct approximation for the total lateral displacement \(\Delta x\) of the emerging ray?

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