Ray Conic Focus

Parallel rays hit a curved mirror and scatter. Drag to change the mirror's shape. At one precise value, eccentricity one: every ray converges to the same point. Find it.

Ray Conic Focus gives you a curved mirror and fourteen beams of light, and asks you to find the shape that focuses them.

The beams approach from the left as parallel horizontal rays. Each one hits the mirror at a different point and reflects according to the law of physics — angle of incidence equals angle of reflection, measured from the surface normal at the exact point of contact. The reflected beams extend across the canvas. At the wrong mirror shape, they scatter in fourteen different directions. A gold ring marks the focus — the target convergence point. Nothing passes through it.

A single horizontal drag changes the mirror's eccentricity. Moving right increases it. The mirror morphs live, from near-circular through increasingly elongated ellipses to the parabola and on to the hyperbola. This family of curves — circle, ellipse, parabola, hyperbola — are not four different objects. They are the same object seen at different angles: cross-sections of a cone at different inclinations, unified by the single parameter the player is adjusting.

As eccentricity approaches one, the scattered beams begin to converge. The amber lines tighten. The gold ring begins to glow as rays thread through it. Then at eccentricity exactly one — the parabola — every ray converges simultaneously to a single point. The chaos resolves. A star appears at the focus from the natural accumulation of fourteen lines meeting at once. The ring erupts.

This is the reflective property of the parabola. It is not an approximation or an average. At eccentricity one, the mathematics forces every parallel ray — regardless of where it strikes the mirror — through exactly one point. For any other eccentricity, the reflection law produces rays that miss the focus. The parabola is unique. The player discovers this not by reading it but by sweeping past it and feeling the convergence arrive and depart.

Every reflecting telescope ever built uses this property. The primary mirror in a Newtonian telescope is parabolic. The Hubble Space Telescope launched in 1990 with a primary mirror ground to the wrong eccentricity — a deviation of two millionths from the correct value — and produced blurry images for three years until a corrective lens was installed. One level in this game replicates that error. The player starts at Hubble's actual eccentricity and must find the exact correction.

The second level approaches the parabola from the other side — starting in hyperbolic territory, where reflected rays diverge in a completely different pattern, and sweeping back toward eccentricity one. The third level requires precision within one and a half hundredths. The fourth is harder still.

No equations. No prior knowledge of optics required. The rays show everything. The gold ring shows where they need to go.

Just the mirror, the light, and the one shape that makes them agree.