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title: "An optical system consists of two thin lenses aligned along a common principal axis. Lens 1 is a converging lens with a focal length of \\(f_1 = +10\\text{ cm}\\), and Lens 2 is a diverging lens with a focal length of \\(f_2 = -10\\text{ cm}\\) placed \\(35\\text{ cm}\\) to the right of Lens 1. An object is placed \\(20\\text{ cm}\\) to the left of Lens 1. What is the location of the final image relative to Lens 2, and what is the total lateral magnification \\(M\\) of the two-lens system?"
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url: "https://nerd-notes.com/ubq/117458/"
date_modified: "2026-08-04T06:52:13+00:00"
---

# An optical system consists of two thin lenses aligned along a common principal axis. Lens 1 is a converging lens with a focal length of \(f_1 = +10\text{ cm}\), and Lens 2 is a diverging lens with a focal length of \(f_2 = -10\text{ cm}\) placed \(35\text{ cm}\) to the right of Lens 1. An object is placed \(20\text{ cm}\) to the left of Lens 1. What is the location of the final image relative to Lens 2, and what is the total lateral magnification \(M\) of the two-lens system?

An optical system consists of two thin lenses aligned along a common principal axis. Lens 1 is a converging lens with a focal length of \(f_1 = +10\text{ cm}\), and Lens 2 is a diverging lens with a focal length of \(f_2 = -10\text{ cm}\) placed \(35\text{ cm}\) to the right of Lens 1. An object is placed \(20\text{ cm}\) to the left of Lens 1. What is the location of the final image relative to Lens 2, and what is the total lateral magnification \(M\) of the two-lens system?

![A horizontal line represents the principal axis. A vertical double-headed arrow labeled Lens 1 sits at an origin position. A second vertical double-headed arrow labeled Lens 2 sits to the right, separated from Lens 1 by a horizontal dimension line labeled \(35\text{ cm}\). To the left of Lens 1, a vertical solid arrow pointing upward stands on the axis, labeled Object and separated from Lens 1 by a horizontal dimension line labeled \(20\text{ cm}\). Lens 1 is annotated with \(f_1 = +10\text{ cm}\) and Lens 2 is annotated with \(f_2 = -10\text{ cm}\). No other labels, lines, text, or optical rays appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785826333-XOgkOW.jpg)

- **A.** \(6\text{ cm}\) to the right of Lens 2 | \(M = +0.4\)
- **B.** \(6\text{ cm}\) to the right of Lens 2 | \(M = -0.4\)
- **C.** \(6\text{ cm}\) to the left of Lens 2 | \(M = -0.4\)
- **D.** \(6\text{ cm}\) to the left of Lens 2 | \(M = +0.4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117458/*