Tangent cone — where it appears
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
The shadow of a ball is a conic
A cone cut by a plane is a conic section — which is the definition of the phrase, not an analogy — and the shadow of a ball is exactly that cut. So the shadow closes or runs to the horizon depending on where the lamp is, and the condition is not what anyone guesses: it is that the lamp is above the top of the ball. The ball's distance appears nowhere in it.
A lamp lights less than half a ball
Everyone knows a sphere is half lit. It is half lit by a source at infinity and by nothing else: a lamp two radii away lights a quarter of it, and the boundary it draws is a circle offset toward the light rather than a great circle. The offset is R²/D, which means a photograph of a lit ball carries the distance to whatever lit it.
Named alongside it
The objects these essays reach for when they reach for this one.
centre of projectionConicDemonstrationPoint lightSilhouetteTerminatorDepth cueHorizonline at infinityRadianceshadow vanishing pointSubtended angle