---
title: "A student uses a thin converging lens to form real images of an object placed at various distances. The student plots the inverse of the image distance \\(\\dfrac{1}{d_i}\\) as a function of the inverse of the object distance \\(\\dfrac{1}{d_o}\\), obtaining the solid line shown in the graph with intercepts at \\(\\dfrac{1}{f_1}\\). The student then replaces the lens with a second thin converging lens having focal length \\(f_2 = 2f_1\\). Which of the following graphs best represents the relationship for the second lens (dashed line) compared to the original lens (solid line)?"
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url: "https://nerd-notes.com/ubq/117528/"
date_modified: "2026-08-04T06:52:40+00:00"
---

# A student uses a thin converging lens to form real images of an object placed at various distances. The student plots the inverse of the image distance \(\dfrac{1}{d_i}\) as a function of the inverse of the object distance \(\dfrac{1}{d_o}\), obtaining the solid line shown in the graph with intercepts at \(\dfrac{1}{f_1}\). The student then replaces the lens with a second thin converging lens having focal length \(f_2 = 2f_1\). Which of the following graphs best represents the relationship for the second lens (dashed line) compared to the original lens (solid line)?

A student uses a thin converging lens to form real images of an object placed at various distances. The student plots the inverse of the image distance \(\dfrac{1}{d_i}\) as a function of the inverse of the object distance \(\dfrac{1}{d_o}\), obtaining the solid line shown in the graph with intercepts at \(\dfrac{1}{f_1}\). The student then replaces the lens with a second thin converging lens having focal length \(f_2 = 2f_1\). Which of the following graphs best represents the relationship for the second lens (dashed line) compared to the original lens (solid line)?

![A quantitative plot with a horizontal axis labeled 1/d_o and a vertical axis labeled 1/d_i, meeting at an origin labeled 0. A solid straight line extends from a point on the vertical axis marked 1/f_1 down and to the right to a point on the horizontal axis marked 1/f_1, forming a line with a slope of -1. Tick marks indicate equal spacing on both axes. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785826359-GlfrIT.jpg)

- **A.** Graph A
- **B.** Graph B
- **C.** Graph C
- **D.** Graph D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117528/*