---
title: "A beam of light in the xy-plane enters an inhomogeneous transparent medium at the origin \\((0,0)\\) traveling into the first quadrant at an angle of \\(45^\\circ\\) above the horizontal \\(+x\\)-axis. The index of refraction \\(n(y)\\) of the medium depends only on the vertical coordinate \\(y\\) and decreases continuously as \\(y\\) increases. Which of the following graphs best represents the path \\(y\\) as a function of \\(x\\) of the light beam as it propagates through the medium?"
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/123440/"
date_modified: "2026-09-28T11:58:36+00:00"
---

# A beam of light in the xy-plane enters an inhomogeneous transparent medium at the origin \((0,0)\) traveling into the first quadrant at an angle of \(45^\circ\) above the horizontal \(+x\)-axis. The index of refraction \(n(y)\) of the medium depends only on the vertical coordinate \(y\) and decreases continuously as \(y\) increases. Which of the following graphs best represents the path \(y\) as a function of \(x\) of the light beam as it propagates through the medium?

A beam of light in the xy-plane enters an inhomogeneous transparent medium at the origin \((0,0)\) traveling into the first quadrant at an angle of \(45^\circ\) above the horizontal \(+x\)-axis. The index of refraction \(n(y)\) of the medium depends only on the vertical coordinate \(y\) and decreases continuously as \(y\) increases. Which of the following graphs best represents the path \(y\) as a function of \(x\) of the light beam as it propagates through the medium?

![A Cartesian coordinate system with a horizontal x-axis and a vertical y-axis meeting at an origin labeled (0,0). Three horizontal dashed lines span across the first quadrant at equally spaced vertical intervals. Above the top dashed line is the label n_3, between the top and middle dashed lines is n_2, and between the middle and bottom dashed lines is n_1. A vertical downward-pointing arrow to the right is labeled n_1 > n_2 > n_3. A single solid straight arrow originates at (0,0) and points upward into the first quadrant at a 45-degree angle to the horizontal axis, labeled Incident ray. An angle arc at the origin between the positive x-axis and this arrow is labeled \theta_0. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-diag-1-1790596715-yb28Xw.jpg)

- **A.** A curve that is concave upward, where the slope \(\dfrac{dy}{dx}\) increases continuously as \(x\) increases.
- **B.** A straight line, where the slope \(\dfrac{dy}{dx}\) remains constant as \(x\) increases.
- **C.** A curve that is concave downward, where the slope \(\dfrac{dy}{dx}\) decreases continuously toward zero as \(x\) increases.
- **D.** An S-shaped curve that is initially concave upward and then becomes concave downward as \(x\) increases.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123440/*