---
title: "A person of height \\(H\\) stands a distance \\(d\\) in front of a flat, vertical plane mirror mounted on a wall. The person can see their entire body (from the top of the head to the bottom of the feet) in a mirror of minimum vertical length \\(L_{\\text{min}}\\). The person then steps backward so that their distance from the mirror increases to \\(2d\\). Which of the following correctly pairs the new minimum vertical mirror length required for the person to see their entire body with the change in the angular size of the image subtended at the person’s eyes?"
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url: "https://nerd-notes.com/ubq/123246/"
date_modified: "2026-09-28T11:58:01+00:00"
---

# A person of height \(H\) stands a distance \(d\) in front of a flat, vertical plane mirror mounted on a wall. The person can see their entire body (from the top of the head to the bottom of the feet) in a mirror of minimum vertical length \(L_{\text{min}}\). The person then steps backward so that their distance from the mirror increases to \(2d\). Which of the following correctly pairs the new minimum vertical mirror length required for the person to see their entire body with the change in the angular size of the image subtended at the person’s eyes?

A person of height \(H\) stands a distance \(d\) in front of a flat, vertical plane mirror mounted on a wall. The person can see their entire body (from the top of the head to the bottom of the feet) in a mirror of minimum vertical length \(L_{\text{min}}\). The person then steps backward so that their distance from the mirror increases to \(2d\). Which of the following correctly pairs the new minimum vertical mirror length required for the person to see their entire body with the change in the angular size of the image subtended at the person's eyes?

![A side-view diagram of an observer standing in front of a vertical wall. On the right, a vertical solid line represents the wall and mirror. On the left, a vertical arrow pointing upward represents a person of height \(H\), standing on a horizontal ground line at a horizontal distance \(d\) from the wall. A double-headed horizontal dimension arrow labeled \(d\) spans between the base of the person and the wall. No rays, reflections, virtual images, or extra construction lines are shown. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596681-CKtJZc.jpg)

- **A.** Minimum vertical mirror length: \(\dfrac{1}{2}H\) | Angular size: Decreases
- **B.** Minimum vertical mirror length: \(\dfrac{1}{2}H\) | Angular size: Remains unchanged
- **C.** Minimum vertical mirror length: \(\dfrac{1}{4}H\) | Angular size: Decreases
- **D.** Minimum vertical mirror length: \(\dfrac{1}{4}H\) | Angular size: Remains unchanged

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123246/*