Why a straw looks bent in a glass of water
Light bends when it passes from air into water, always at one very specific angle for a given pair of materials. Why that particular angle, and not a straight line or some other bend? Pierre de Fermat proposed an explanation in 1662 that had nothing to do with geometry for its own sake.
Reveal the answer
Fermat argued light always takes whichever path takes the least time between two points, not the shortest distance. Because light travels slower in water than in air, the fastest route bends at the surface, trading a little extra distance in the slow medium for a lot less time overall, the same logic a lifeguard uses sprinting at an angle on sand to reach a swimmer fastest rather than running straight at them. Fermat's principle of least time correctly predicts the exact law of refraction that had only been described empirically before.
— Pierre de Fermat, Correspondence on the principle of least time — 1662