---
title: "A student conducts an experiment to determine the radius of curvature \\(R\\) of a concave spherical mirror using an optical bench. The student places an illuminated object at several positions such that \\(d_o > f\\) and records the corresponding distances \\(d_i\\) to a viewing screen where sharp real images are formed. The student linearizes the data by plotting \\(\\dfrac{1}{d_i}\\) on the vertical axis as a function of \\(\\dfrac{1}{d_o}\\) on the horizontal axis. Which of the following correctly identifies the theoretical slope of the best-fit line and the relationship used to determine the radius of curvature \\(R\\) from the vertical intercept \\(b\\)?"
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url: "https://nerd-notes.com/ubq/123268/"
date_modified: "2026-09-28T11:58:03+00:00"
---

# A student conducts an experiment to determine the radius of curvature \(R\) of a concave spherical mirror using an optical bench. The student places an illuminated object at several positions such that \(d_o > f\) and records the corresponding distances \(d_i\) to a viewing screen where sharp real images are formed. The student linearizes the data by plotting \(\dfrac{1}{d_i}\) on the vertical axis as a function of \(\dfrac{1}{d_o}\) on the horizontal axis. Which of the following correctly identifies the theoretical slope of the best-fit line and the relationship used to determine the radius of curvature \(R\) from the vertical intercept \(b\)?

A student conducts an experiment to determine the radius of curvature \(R\) of a concave spherical mirror using an optical bench. The student places an illuminated object at several positions such that \(d_o > f\) and records the corresponding distances \(d_i\) to a viewing screen where sharp real images are formed. The student linearizes the data by plotting \(\dfrac{1}{d_i}\) on the vertical axis as a function of \(\dfrac{1}{d_o}\) on the horizontal axis. Which of the following correctly identifies the theoretical slope of the best-fit line and the relationship used to determine the radius of curvature \(R\) from the vertical intercept \(b\)?

![A horizontal line represents the optical bench axis. On the right, a concave spherical mirror is shown as a vertical curved arc with its reflective concave surface facing left. Along the axis to the left of the mirror, two tick marks are labeled F and C, where F is located a distance f from the mirror vertex and C is located a distance 2f from the vertex. To the left of C, a vertical upward-pointing arrow represents the illuminated object. A horizontal double-headed dimension arrow below the axis extends from the object arrow to the mirror vertex, labeled d_o. A vertical rectangular viewing screen stands between F and C, with a horizontal double-headed dimension arrow extending from the screen to the mirror vertex, labeled d_i. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596683-VIWf2l.jpg)

- **A.** The slope is \(-1\), and the radius of curvature is \(R = \dfrac{2}{b}\).
- **B.** The slope is \(-1\), and the radius of curvature is \(R = \dfrac{1}{b}\).
- **C.** The slope is \(+1\), and the radius of curvature is \(R = \dfrac{2}{b}\).
- **D.** The slope is \(+1\), and the radius of curvature is \(R = \dfrac{1}{2b}\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123268/*