---
title: "A ray of monochromatic light traveling in a transparent material with index of refraction \\(n_1\\) strikes the flat boundary of a parallel-sided slab with index of refraction \\(n_2\\) at an angle of incidence \\(\\theta_1\\) relative to the normal. The light refracts into the middle slab, travels through it, and then enters a third parallel-sided slab with index of refraction \\(n_3\\). All boundaries between the media are parallel to one another. Which of the following expressions correctly gives the angle of refraction \\(\\theta_3\\) in the third slab?"
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url: "https://nerd-notes.com/ubq/116805/"
date_modified: "2026-08-04T06:09:44+00:00"
---

# A ray of monochromatic light traveling in a transparent material with index of refraction \(n_1\) strikes the flat boundary of a parallel-sided slab with index of refraction \(n_2\) at an angle of incidence \(\theta_1\) relative to the normal. The light refracts into the middle slab, travels through it, and then enters a third parallel-sided slab with index of refraction \(n_3\). All boundaries between the media are parallel to one another. Which of the following expressions correctly gives the angle of refraction \(\theta_3\) in the third slab?

A ray of monochromatic light traveling in a transparent material with index of refraction \(n_1\) strikes the flat boundary of a parallel-sided slab with index of refraction \(n_2\) at an angle of incidence \(\theta_1\) relative to the normal. The light refracts into the middle slab, travels through it, and then enters a third parallel-sided slab with index of refraction \(n_3\). All boundaries between the media are parallel to one another. Which of the following expressions correctly gives the angle of refraction \(\theta_3\) in the third slab?

![A rectangular diagram showing three stacked horizontal layers of transparent media labeled from top to bottom as Medium 1 with index \(n_1\), Medium 2 with index \(n_2\), and Medium 3 with index \(n_3\). The horizontal boundaries between the layers are parallel. A single straight light ray enters Medium 1 from the upper left, traveling downward and to the right toward the boundary between Medium 1 and Medium 2. A dashed vertical line perpendicular to the upper horizontal boundary represents the normal at the point of incidence. The angle between the incoming light ray and this normal line is labeled \(\theta_1\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785823784-0MJygo.jpg)

- **A.** \(\arcsin\left( \dfrac{n_1 n_2}{n_3^2} \sin\theta_1 \right)\)
- **B.** \(\arcsin\left( \dfrac{n_2}{n_3} \sin\theta_1 \right)\)
- **C.** \(\arcsin\left( \dfrac{n_1}{n_3} \sin\theta_1 \right)\)
- **D.** \(\arcsin\left( \dfrac{n_3}{n_1} \sin\theta_1 \right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116805/*