---
title: "Hall of Mirrors Interactive Lab | Sandbox Physics"
description: "Which virtual images can an observer actually see as mirrors move? Only the images whose reflected rays actually land on the mirrors and travel on to your eye."
canonical_url: "https://sandboxphysics.com/labs/hall-of-mirrors/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/hall-of-mirrors/"
last_modified: "2026-10-27"
---

Optics 002 · Ray worlds, boundaries, and natural optics

# Hall of Mirrors

**Which virtual images can an observer actually see as mirrors move?** Only the images whose reflected rays actually land on the mirrors and travel on to your eye. A flat mirror always makes an image the same size as the object, but whether you can see a given image depends on how big the mirrors are, where they sit and what blocks the view.

In a labeled mirror gallery, exact plane reflection builds the images formed by a single mirror, a mirror corridor and a kaleidoscope. Real and virtual objects share one geometry and scale; color, opacity, the actual light paths and backward construction lines show which is which.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

The ideal image count for mirrors at an angle assumes the mirrors are infinite. For the finite rectangular panels, each image is tested geometrically against the mirror edges, and the number of candidate images is reported separately.

Physics tutorial

## Audit the physics of Hall of Mirrors

**Background** A plane mirror forms its image by reflecting each point of the object across the mirror plane: $\mathbf x^{\prime}=\mathbf x-2\mathbf n\bigl[\mathbf n\cdot(\mathbf x-\mathbf p)\bigr]$. With two mirrors, repeating this reflection produces a whole family of images. Real panels have finite size, so only some of the construction rays traced back toward those images pass through a mirror.

**Why it matters** Which virtual images can an observer actually see as mirrors move?

Start with the essentials

- **Focus question**: Which virtual images can an observer actually see as mirrors move?
- **One-sentence intuition**: A plane mirror keeps the complete geometry of the object, so its lateral magnification is $m=+1$. The Lab may draw a virtual image translucent or in another color to make it easy to pick out, but never smaller than the object.

### Core mathematical model

#### Reflection across a plane

$$
\mathbf x^{\prime}=\mathbf x-2\mathbf n\bigl[\mathbf n\cdot(\mathbf x-\mathbf p)\bigr]
$$

The mirror's unit normal and one point on it fix exactly where the virtual image sits.

#### Plane-mirror magnification

$$
m=\frac{h_i}{h_o}=+1
$$

The image is upright and the same physical size as the object; its distance behind the plane equals the object distance in front.

#### Image count for two ideal mirrors

$$
N_{\mathrm{ideal}}\approx\frac{2\pi}{\alpha}-1
$$

This count is exact only for particular mirror angles and object positions, so the Lab labels it as an ideal value.

### Common difficulties

#### Thinking a virtual image gives off light

**Typical misconception** The virtual image sends light outward from the place where it appears.

**Better mental model** The dashed sight line traced back behind the mirror is only a construction. Real light reaches the observer only after it reflects off a real mirror panel.

### Run the experiment

1. 01

   #### Scene 1: Single virtual image

   Move the observer laterally in the single-mirror scene and compare the object and image distances to the mirror plane.

   **What to observe:** As the observer moves, the sight line changes, but the image stays as far behind the mirror as the object is in front, and exactly as tall.

2. 02

   #### Scene 2: Infinite mirror corridor

   Change the corridor angle and follow the images outward from the real object, one reflection order at a time.

   **What to observe:** A smaller mirror angle gives more ideal images, but the finite panels drop any construction point that falls outside their edges.

3. 03

   #### Scene 3: Kaleidoscope symmetry

   In the kaleidoscope scene, check two things separately: whether the image pattern closes up around the full circle, and which images pass the observer-aperture test.

   **What to observe:** A closed pattern can hold more ideal images than the finite mirrors accept as candidates.

Physical conclusion

Three questions stay separate: where the equal-size image sits, whether the finite mirrors let its rays through, and whether the observer can see all of it. A correct picture answers all three.

Waves & optics · Starter path

## From one ray to interference measurement

Start with refraction, find where the ray picture stops working, then use interference to measure tiny distances.

[Start here → **Optical Boundary Explorer** Turn the incident angle and watch reflected and transmitted power trade off. Then switch to the critical-angle scene. Observe · 11 min](https://sandboxphysics.com/labs/optical-boundary-explorer/)

1. [1 Optical Boundary Explorer](https://sandboxphysics.com/labs/optical-boundary-explorer/)
2. [2 Rainbow Caustic Observatory](https://sandboxphysics.com/labs/rainbow-laboratory/)
3. [3 Camera Obscura](https://sandboxphysics.com/labs/camera-obscura/)
4. [4 Coherent Wave Composer](https://sandboxphysics.com/labs/coherent-wave-composer/)
5. [5 Young Double-Slit Bench](https://sandboxphysics.com/labs/young-double-slit-bench/)
6. [6 Michelson Precision Lab](https://sandboxphysics.com/labs/michelson-precision-lab/)

[View the full path →](https://sandboxphysics.com/topics/waves-and-optics/#starter-path)