---
title: "A monochromatic light ray traveling in air \\(n_{\\text{air}} \\approx 1\\) strikes a flat, parallel-sided glass plate of thickness \\(d\\) and index of refraction \\(n\\) at a small angle of incidence \\(\\theta\\) relative to the normal line. After passing through the plate and emerging back into air, the ray is parallel to its original incident direction but is shifted laterally by a perpendicular distance \\(x\\). Using the small-angle approximations \\(\\sin\\theta \\approx \\tan\\theta \\approx \\theta\\) (where \\(\\theta\\) is in radians) and \\(\\cos\\theta \\approx 1\\), which of the following is a correct expression for the lateral displacement \\(x\\)?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/116862/"
date_modified: "2026-08-04T06:09:53+00:00"
---

# A monochromatic light ray traveling in air \(n_{\text{air}} \approx 1\) strikes a flat, parallel-sided glass plate of thickness \(d\) and index of refraction \(n\) at a small angle of incidence \(\theta\) relative to the normal line. After passing through the plate and emerging back into air, the ray is parallel to its original incident direction but is shifted laterally by a perpendicular distance \(x\). Using the small-angle approximations \(\sin\theta \approx \tan\theta \approx \theta\) (where \(\theta\) is in radians) and \(\cos\theta \approx 1\), which of the following is a correct expression for the lateral displacement \(x\)?

A monochromatic light ray traveling in air \(n_{\text{air}} \approx 1\) strikes a flat, parallel-sided glass plate of thickness \(d\) and index of refraction \(n\) at a small angle of incidence \(\theta\) relative to the normal line. After passing through the plate and emerging back into air, the ray is parallel to its original incident direction but is shifted laterally by a perpendicular distance \(x\). Using the small-angle approximations \(\sin\theta \approx \tan\theta \approx \theta\) (where \(\theta\) is in radians) and \(\cos\theta \approx 1\), which of the following is a correct expression for the lateral displacement \(x\)?

![A rectangular glass slab of thickness d is shown in cross-section with horizontal top and bottom boundaries. A light ray traveling from the upper-left hits the top boundary at an angle \theta relative to the vertical normal line. Inside the slab, the ray bends toward the normal line at an angle \theta_2 relative to the vertical. The ray exits the bottom boundary and continues to the lower-right parallel to the incident ray path. A dashed line extends the path of the original incident ray straight through the slab. A perpendicular double-headed arrow labeled x spans the distance between the extended original path and the actual emerging ray. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785823793-4wKsEP.jpg)

- **A.** \(x = d\theta\left(1 - \dfrac{1}{n}\right)\)
- **B.** \(x = d\theta\left(1 - n\right)\)
- **C.** \(x = \dfrac{d\theta}{n}\)
- **D.** \(x = d\theta\left(1 + \dfrac{1}{n}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116862/*