Optimal Mirascope Geometry — Ray Trace Simulator & Research

The parabola is not the optimal mirror shape for maximizing mirascope viewing angle.

Principle 1 — Light travels in straight lines.

Principle 2 — Angle in equals angle out.

In 1969, a custodial worker at UC Santa Barbara was cleaning a storage closet filled with old military searchlight mirrors when he saw something strange — dust that seemed to float in the air and couldn't be wiped away. A physicist identified it as a real image, an optical effect where light comes together so precisely that it makes something appear to be there even when it's not. This accidental discovery led to the creation of the mirascope, and the parabolic shape of those surplus mirrors has been the basis for every version made since then.

Over the next few decades, researchers found that parabolas have a special mathematical property: any light ray coming from the focal point bounces off perfectly parallel to the axis, and the other way around. This property is exact and makes the mirascope's image very sharp. However, a small assumption was overlooked. Since the parabola creates a perfect focus, it was considered the best mirror shape for the device. Nobody made a distinction between making the focus as precise as possible and making the experience better for the viewer. These are actually two different problems. Every parabolic mirascope built has a viewing angle of about 55 degrees from horizontal. This angle is a result of the parabolic shape, not a fundamental law of optics.

This project starts with a basic idea: the only physical rules that apply to the mirascope are that light moves in straight lines and bounces back at the same angles. The parabolic shape and the need for rays to travel parallel between the mirrors, as well as the 55-degree viewing limit, are all results of one specific geometric solution, not limits set by physics. A different mirror shape could send light along completely different paths and still bring the rays together at the image point, even if no human designer would think of drawing those paths. Such a shape might be able to trade some of the parabola's perfect focus for a wider viewing area, especially when the object is small and gives off its own light, and a slightly blurry image would be okay if it means being able to see it from more angles.

The tools needed to search for a shape like this, such as evolutionary algorithms that can explore millions of freeform surface geometries, exact ray-tracing engines that can evaluate each one, and multi-objective scoring that balances image quality with viewing angle and brightness, did not exist when the mirascope was first discovered. They were also not available for practical use when it was last studied in 2007. However, these tools are available now. This project plans to use them, starting with the two basic laws of reflection and making no assumptions about the mirror shape, to explore a question that has never been asked before: is the parabola really the best shape for a mirascope, or was it just the shape that was readily available?

Simulator Math three functions · all geometry derives from these

① Surface Normal of a Parabola Mirror surface: y = x² / (4f) Slope at x: dy/dx = x / (2f) Normal vector: n = ( −x/2f , 1 ) normalized to unit length Top mirror (M2) flips y-component sign to −1

② Reflection Formula r = d − 2(d·n)n d = incoming ray direction · n = surface normal · r = reflected ray direction Standard specular reflection. Confirmed: Wikipedia / optics literature.

③ Ray–Parabola Intersection Ray: x(t) = ox + t·dx y(t) = oy + t·dy Substitute into parabola equation → quadratic in t → two solutions Selection: smallest positive t (nearest intersection) ⚠ Open question: is smallest t always the correct root for a concave mirror? Needs expert review.

Research Audit Log parabolic mirascope · optimal geometry search · Elijah · 2026

2026-05-06 #1 BASELINE — single point, h=0, 20 rays, ap/D fixed 0.15 f₁/d=1.000 · f₂/d=1.000 · ap/D=0.150 → cone 44° Canonical symmetric mirascope. Every commercial unit uses this. Established baseline.

2026-05-06 #2 FIRST ASYMMETRIC FIND — convergence bug present f₁/d=0.820 · f₂/d=1.120 · d=100mm → cone 53° ⚠ image not confirmed above aperture Optimizer found asymmetric config but validity check allowed image below aperture. Discarded.

2026-05-06 #3 SINGLE POINT · image-above-aperture fix applied · 20 rays f₁/d=0.917 · f₂/d=1.079 · ap/D=0.080 → window 55.05° (23.45°–78.50°) First clean result. Asymmetry confirmed. Small aperture wins. Canonical is not optimal.

2026-05-06 #4 3-POINT OBJECT · ap/D as search variable · coarse+refine · 20 rays f₁/d=0.917 · f₂/d=1.079 · ap/D=0.080 → window 55.05° (23.45°–78.50°) 3-point intersection added. Ratios held from run 3 — result is stable. Aperture ratio confirmed at 0.08.

2026-05-06 #5 3-POINT OBJECT · ap/D variable · hard imgY=0 · 40 rays · d_sep 60–150mm f₁/d=0.9290 · f₂/d=1.0850 · ap/D=0.100 · d=60mm → window 57.99° (22.56°–80.54°) Ratios stable vs 20-ray result. 32% wider than canonical. d_sep hitting floor of search range at 60mm — needs investigation.

2026-05-06 #6 CONFIRMED — d_sep range extended to 30mm · ratios held · parabolic ceiling set f₁/d=0.9230 · f₂/d=1.0910 · ap/D=0.100 · d=40mm → window 58.18° (22.29°–80.47°) d_sep dropped to 40mm but window width unchanged at ~58°. Ratios shifted <1% across all runs. Three independent confirmations of same answer. Parabolic ceiling is real and confirmed.

KEY FINDINGS — parabolic family ceiling CONFIRMED

① Optimal parabolic mirascope is asymmetric — f₁ ≠ f₂. Every commercial unit uses identical mirrors. That is suboptimal.

② Confirmed ratios: f₁/d ≈ 0.923 · f₂/d ≈ 1.091 — bottom mirror shorter, top longer. Stable across 6 runs.

③ Optimal aperture = 10% of mirror diameter, not the typical 15–20%.

④ d_sep does not affect viewing window width — only device scale. Ratios are all that matter.

⑤ True viewing window for whole object: ~58° vs canonical ~44° — 32% improvement within parabolic family.

⑥ These are dimensionless ratios — multiply by any d_sep to get real dimensions.

⬡ Parabolic phase complete. Ceiling confirmed at ~58°. Non-parabolic search is next phase.

Research Checklist mirascope optimal geometry · all phases · Elijah · 2026

PHASE 1 — PARABOLIC FAMILY ✓ COMPLETE · ceiling 58.18°

✓Canonical symmetric config (f1=f2=d_sep) — baseline 44° ✓Asymmetric focal lengths (f1 ≠ f2) — optimal f1/d=0.923 · f2/d=1.091 ✓Aperture ratio as free variable — optimal ap/D=0.10 ✓Separation distance range — scale only, ratios are all that matter ✓Multi-point object (3 heights, intersection) — window 58.18° ✓Edge trimming — subsumed by ap/D=0.10 finding ✓Raised separation / larger device — subsumed by d_sep scale finding —Curved edges — skip · fabrication not optics · no sim model

PHASE 2 — PATH GEOMETRY ○ NOT STARTED

☐4-bounce paths — does longer path produce wider exit angles? ☐6-bounce paths — secondary images, wider still? ☐Aperture location — off-center, bottom mirror, side ☐Aperture shape — circular vs slot vs annular ring

PHASE 3 — MIRROR CONFIGURATION ○ NOT STARTED

☐Symmetric axis tilt — mirrors angled toward each other (V shape) ☐Lateral offset — top mirror shifted off-axis ☐One mirror flat, one concave — hybrid configuration ☐Unequal mirror diameters — top and bottom different sizes

PHASE 4 — NON-PARABOLIC SHAPES ○ NOT STARTED · requires new simulator

☐Spherical mirrors — simpler to manufacture, how much do they lose? ☐Elliptical mirrors — different conic section ☐Freeform surface — control points, optimizer finds the shape ☐Composite surface — parabolic center, different curve at rim

OPEN QUESTIONS

? Does optimal shape change with object size ratio?

? Is there a theoretical maximum viewing angle from first principles?

? Do 4-bounce paths share the same image point as 2-bounce paths?

? Can aperture location and mirror tilt be co-optimized?

? Does the asymmetric optimum (f1≠f2) hold for non-parabolic shapes?