Ladder
Imaging — the ladder
2 distinct arguments against one idea, from the one that introduces it to the one that assumes the rest.
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What a lens is doing, and why three rays are enough
A lens bends every ray that reaches it. The construction uses three, because three are all that can be drawn without calculation — and any three that meet prove all the rest do.
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The mirror that cannot focus, and the shape that can
A perfect sphere does not bring parallel light to a point. The blur is not a manufacturing defect — it is what the shape does, and the shape is used anyway, for a reason worth knowing.