---
title: "Three thin, converging biconvex lenses—Lens 1, Lens 2, and Lens 3—are manufactured with identical geometric dimensions and surface radii of curvature. The lenses are made of three different transparent materials with indices of refraction \\(n_1 = 1.4\\), \\(n_2 = 1.6\\), and \\(n_3 = 1.8\\), respectively. Each lens is placed in air (\\(n_{\\text{air}} = 1.0\\)), and a beam of parallel light rays is directed along the principal axis of each lens. Which of the following correctly ranks the focal lengths \\(f_1\\), \\(f_2\\), and \\(f_3\\) of the three lenses?"
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/116877/"
date_modified: "2026-08-04T06:09:57+00:00"
---

# Three thin, converging biconvex lenses—Lens 1, Lens 2, and Lens 3—are manufactured with identical geometric dimensions and surface radii of curvature. The lenses are made of three different transparent materials with indices of refraction \(n_1 = 1.4\), \(n_2 = 1.6\), and \(n_3 = 1.8\), respectively. Each lens is placed in air (\(n_{\text{air}} = 1.0\)), and a beam of parallel light rays is directed along the principal axis of each lens. Which of the following correctly ranks the focal lengths \(f_1\), \(f_2\), and \(f_3\) of the three lenses?

Three thin, converging biconvex lenses—Lens 1, Lens 2, and Lens 3—are manufactured with identical geometric dimensions and surface radii of curvature. The lenses are made of three different transparent materials with indices of refraction \(n_1 = 1.4\), \(n_2 = 1.6\), and \(n_3 = 1.8\), respectively. Each lens is placed in air (\(n_{\text{air}} = 1.0\)), and a beam of parallel light rays is directed along the principal axis of each lens. Which of the following correctly ranks the focal lengths \(f_1\), \(f_2\), and \(f_3\) of the three lenses?

![Three identical vertical biconvex lenses are arranged in a horizontal row, labeled Lens 1, Lens 2, and Lens 3 from left to right. Each lens is drawn as a symmetric convex shape bounded by two circular arc curves meeting at top and bottom points. Lens 1 is labeled with index of refraction \(n_1 = 1.4\), Lens 2 with \(n_2 = 1.6\), and Lens 3 with \(n_3 = 1.8\). A horizontal dashed line representing the principal axis passes through the geometric center of all three lenses. For each lens, two horizontal parallel arrows pointing to the right approach the left curved surface from air, one above the principal axis and one below the principal axis. No light rays or focal points are shown to the right of any lens. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785823797-dBAQzB.jpg)

- **A.** \(f_3 > f_2 > f_1\)
- **B.** \(f_1 = f_2 = f_3\)
- **C.** \(f_2 > f_1 > f_3\)
- **D.** \(f_1 > f_2 > f_3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116877/*