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title: "A concave spherical mirror and a convex spherical mirror each have a radius of curvature of magnitude \\(R\\). An upright object of height \\(h\\) is placed at a distance \\(d = R\\) along the central optical axis in front of the concave mirror, forming an image of height \\(h_{\\text{concave}}\\). The same object is then placed at a distance \\(d = R\\) along the central optical axis in front of the convex mirror, forming an image of height \\(h_{\\text{convex}}\\). What is the ratio \\(\\dfrac{h_{\\text{concave}}}{h_{\\text{convex}}}\\) of the heights of the two images?"
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url: "https://nerd-notes.com/ubq/123320/"
date_modified: "2026-09-28T11:58:09+00:00"
---

# A concave spherical mirror and a convex spherical mirror each have a radius of curvature of magnitude \(R\). An upright object of height \(h\) is placed at a distance \(d = R\) along the central optical axis in front of the concave mirror, forming an image of height \(h_{\text{concave}}\). The same object is then placed at a distance \(d = R\) along the central optical axis in front of the convex mirror, forming an image of height \(h_{\text{convex}}\). What is the ratio \(\dfrac{h_{\text{concave}}}{h_{\text{convex}}}\) of the heights of the two images?

A concave spherical mirror and a convex spherical mirror each have a radius of curvature of magnitude \(R\). An upright object of height \(h\) is placed at a distance \(d = R\) along the central optical axis in front of the concave mirror, forming an image of height \(h_{\text{concave}}\). The same object is then placed at a distance \(d = R\) along the central optical axis in front of the convex mirror, forming an image of height \(h_{\text{convex}}\). What is the ratio \(\dfrac{h_{\text{concave}}}{h_{\text{convex}}}\) of the heights of the two images?

![Two diagrams arranged vertically. The upper diagram shows a horizontal principal axis line with a vertical curved arc representing a concave spherical mirror facing left. Ticks on the axis to the left of the mirror mark the focal point labeled F at distance R/2 and the center of curvature labeled C at distance R. A vertical upward-pointing solid arrow representing an object of height h stands at C. The lower diagram shows a horizontal principal axis line with a vertical curved arc representing a convex spherical mirror bulging toward the left. Ticks on the axis to the right of the mirror mark the focal point labeled F at distance R/2 and the center of curvature labeled C at distance R. A vertical upward-pointing solid arrow of height h stands to the left of the mirror at distance R. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596688-1dLt5r.jpg)

- **A.** \(\dfrac{1}{3}\)
- **B.** \(1\)
- **C.** \(2\)
- **D.** \(3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123320/*