---
title: "A group of students is tasked with experimentally determining the focal length \\( f \\) of a converging lens. They are provided with an optics bench (a long track with a meterstick attached), the converging lens mounted on a holder, an illuminated object (a light source with a distinct geometric pattern), and a white viewing screen. All components can slide along the track and their positions can be read from the attached meterstick."
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url: "https://nerd-notes.com/ubq/117714/"
date_modified: "2026-08-04T07:53:36+00:00"
---

# A group of students is tasked with experimentally determining the focal length \( f \) of a converging lens. They are provided with an optics bench (a long track with a meterstick attached), the converging lens mounted on a holder, an illuminated object (a light source with a distinct geometric pattern), and a white viewing screen. All components can slide along the track and their positions can be read from the attached meterstick.

A group of students is tasked with experimentally determining the focal length \( f \) of a converging lens. They are provided with an optics bench (a long track with a meterstick attached), the converging lens mounted on a holder, an illuminated object (a light source with a distinct geometric pattern), and a white viewing screen. All components can slide along the track and their positions can be read from the attached meterstick.

![An optics bench extending horizontally. From left to right on the bench are three components: an illuminated object (a box with a crosshair pattern on its right face), a converging lens mounted vertically in a circular holder, and a flat vertical viewing screen. A meterstick runs along the bottom of the bench. The objects are aligned along the same central horizontal optical axis.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830015-tmrLJ8.jpg)

**Part a)** **Describe** an experimental procedure the students could use to collect the necessary data to determine the focal length of the converging lens. In your description, **identify** what measurements will be made, how the independent variable will be varied, and how the students can minimize experimental error. Do not write a step-by-step list; write your procedure in a coherent paragraph. *(3 points)*

**Part b)** The students intend to graph their data to produce a straight line. **Indicate** which quantities should be graphed on the vertical and horizontal axes so that the focal length \( f \) can be determined directly from the intercepts of the best-fit line. - Vertical axis: - Horizontal axis: *(1 points)*

**Part c)** The students collect the data shown in the table below, where \( d_o \) is the object distance and \( d_i \) is the image distance. | Trial | \( d_o \text{ (cm)} \) | \( d_i \text{ (cm)} \) | |-------|------------------------|------------------------| | 1     | 15.0                   | 30.5                   | | 2     | 20.0                   | 20.2                   | | 3     | 25.0                   | 16.5                   | | 4     | 30.0                   | 15.2                   | | 5     | 40.0                   | 13.5                   | *(3 points)*

**Part d)** Using your best-fit line, **determine** an experimental value for the focal length \( f \) of the lens. *(2 points)*

**Part e)** A second group of students performs the same experiment. However, the converging lens they use has a significant thickness \( t \). The students mistakenly measure the object distance \( d_o \) from the illuminated object to the front surface of the lens, and the image distance \( d_i \) from the screen to the back surface of the lens, rather than measuring to the optical center of the lens. **Justify** whether this systematic error will cause their calculated value for the focal length \( f_{\text{calc}} \) to be greater than, less than, or equal to the actual focal length \( f_{\text{true}} \) of the lens. *(3 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117714/*