---
title: "An optical element is constructed using a plano-convex lens made of glass with an index of refraction \\(n > 1\\) and a curved surface with radius of curvature \\(R\\). Two silvering configurations are prepared:  – **System 1:** The flat back surface of the lens is silvered, so incoming parallel light rays refract at the curved front surface, reflect off the flat back surface, and refract again upon exiting the curved surface. – **System 2:** The outer curved front surface of the lens is silvered, so incoming parallel light rays strike the silvered curved surface directly.  Which of the following correctly indicates whether the focal length of each system depends on the index of refraction \\(n\\) of the glass?"
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url: "https://nerd-notes.com/ubq/116927/"
date_modified: "2026-08-04T06:10:09+00:00"
---

# An optical element is constructed using a plano-convex lens made of glass with an index of refraction \(n > 1\) and a curved surface with radius of curvature \(R\). Two silvering configurations are prepared:

– **System 1:** The flat back surface of the lens is silvered, so incoming parallel light rays refract at the curved front surface, reflect off the flat back surface, and refract again upon exiting the curved surface.
– **System 2:** The outer curved front surface of the lens is silvered, so incoming parallel light rays strike the silvered curved surface directly.

Which of the following correctly indicates whether the focal length of each system depends on the index of refraction \(n\) of the glass?

An optical element is constructed using a plano-convex lens made of glass with an index of refraction \(n > 1\) and a curved surface with radius of curvature \(R\). Two silvering configurations are prepared:

- **System 1:** The flat back surface of the lens is silvered, so incoming parallel light rays refract at the curved front surface, reflect off the flat back surface, and refract again upon exiting the curved surface.
- **System 2:** The outer curved front surface of the lens is silvered, so incoming parallel light rays strike the silvered curved surface directly.

Which of the following correctly indicates whether the focal length of each system depends on the index of refraction \(n\) of the glass?

![A side-by-side cross-sectional schematic showing System 1 on the left and System 2 on the right. System 1 features a plano-convex lens shape with a curved boundary facing left and a vertical flat boundary on the right. The vertical flat boundary has diagonal hatching along its right side to represent a reflective mirror coating. Parallel horizontal rays entering from the left refract at the curved boundary, reflect off the flat back boundary, and exit to the left. System 2 features the same plano-convex lens shape, but the curved boundary facing left has diagonal hatching along its outer left surface to represent a reflective mirror coating. Parallel horizontal rays entering from the left reflect directly off the outer curved silvered surface without passing through the lens material. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785823809-IPgaaV.jpg)

- **A.** System 1: Independent of \(n\) ; System 2: Independent of \(n\)
- **B.** System 1: Independent of \(n\) ; System 2: Depends on \(n\)
- **C.** System 1: Depends on \(n\) ; System 2: Independent of \(n\)
- **D.** System 1: Depends on \(n\) ; System 2: Depends on \(n\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116927/*