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Sandbox Physics

Optics 006 · Ray worlds, boundaries, and natural optics

Floating Image Mirascope

A close cutaway mirascope labels both confocal paraboloids, the central opening, the hidden point object, and the luminous real-image point. Color-separated path segments make the two reflections, middle collimation, aperture clipping, and free-space crossing readable at a glance.

Interactive modelFloating Image Mirascope
Captured solid angle ηΩ\eta_{\Omega}0.500.50
Real-image height himageh_{\mathrm{image}}50%50\%
Optical-path spread ΔOPL\Delta\mathrm{OPL}0.00π0.00\pi
Model regimevalid model regime\text{valid model regime}

Physics tutorial

Audit the physics of Floating Image Mirascope

BackgroundA mirascope uses two opposed confocal paraboloids. Each surface follows z=r24fz=\frac{r^2}{4f}: the upper reflection collimates light from the hidden object, and the lower reflection brings that parallel family to the opening as a real image.

Why it mattersWhere must two parabolic mirrors place a real image that can be seen but not touched?

Start with the essentials

Focus question
Where must two parabolic mirrors place a real image that can be seen but not touched?
One-sentence intuition
For the ideal confocal trace, all accepted rays share ΔOPL=0\Delta\mathrm{OPL}=0. Aperture clipping changes captured solid angle and brightness, not the geometric image location.

Core mathematical model

Paraboloid profile

z=r24fz=\frac{r^2}{4f}

The generated mirror mesh and its reflection normal use the same focal length.

Equal optical path

OPL=∑jnjℓj,ΔOPL=0\mathrm{OPL}=\sum_j n_j\ell_j,\qquad \Delta\mathrm{OPL}=0

In the ideal air-filled confocal geometry, accepted ray paths from object to image have equal total length.

Collected solid-angle fraction

ηΩ=Ωaccepted2π\eta_{\Omega}=\frac{\Omega_{\mathrm{accepted}}}{2\pi}

This hemisphere fraction quantifies aperture capture without pretending that all emitted directions reach the image.

Common difficulties

Treating the floating image as a hologram

Typical misconceptionThe image is a screen effect or a virtual image that exists only for one viewpoint.

Better mental modelThe traced rays physically converge in free space above the opening, forming a real image. Viewpoint changes alter which rays enter the eye, not the convergence point.

Run the experiment

  1. 01

    Scene 1: Open mirascope

    Follow one color sequence from the hidden object to the upper mirror, down the collimated middle segment, and from the lower mirror to the free-space image point.

    What to observe: Every accepted path has one upper and one lower reflection before crossing the same real-image point.
  2. 02

    Scene 2: Aperture clipping

    Reduce the outer mirror aperture and distinguish it from the separately labeled central opening.

    What to observe: Clipping removes high-angle rays and reduces collected solid angle, while image height remains tied to focal length.
  3. 03

    Scene 3: Walk-around parallax

    Orbit the camera around the walk-around scene while keeping the optical geometry fixed.

    What to observe: The real image remains spatially fixed during camera orbit; only its visible ray subset and parallax change.