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.

Ideal image order

N_{\mathrm{ideal}}

$0.50$

Finite-aperture candidates

N_{\mathrm{aperture}}

$50\%$

Reflection residual

\Delta_{\mathrm{refl}}

$0.00\pi$

Model regime $\text{valid model regime}$

Physics tutorial

Audit the physics of Hall of Mirrors

BackgroundA 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 mattersWhich 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 misconceptionThe virtual image sends light outward from the place where it appears.

Better mental modelThe 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

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.
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.
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.