Physics

Why light bends in water: the lifeguard's shortest-time path (Fermat's principle)

A dashed orange path bends at a shoreline between sand and water, joining a lifeguard and a swimmer
30seconds
The 30-second version

A lifeguard runs faster than she swims, so the quickest route to a swimmer is not a straight line. It bends at the shoreline, and the bend follows one tidy rule.

Light obeys the same rule when it enters water or glass. That rule is Snell's law, and Fermat's principle explains it: light takes the path that needs the least time.

Drag the entry point yourself, watch the time curve, and find the bend that wins.

Deep dive · 4 min
Deep dive · 4 min

More in Physics

View all →
Why a spinning ball curves in mid-air: the Magnus effect Clip a football with the side of your boot and it bends around a wall with nothing touching it in the air. A spinning ball drags air around with its surface… Physics5 min read Why a boat's wake is always a 39° V: Kelvin's wedge Behind every boat spreads a V of ripples, and it is always about 39° wide, whether the boat crawls or speeds. Lord Kelvin worked out why in 1887: only waves… Physics4 min read Why the bottom of a dropped Slinky hangs in mid-air: a wave has to bring the news Hold a Slinky by its top, let it stretch, and let go. The top rushes down while the bottom coil hovers, apparently ignoring gravity, until the collapsing coils… Physics5 min read Why a dried coffee drop leaves a ring: the edge is stuck and the rim dries first Spill coffee, let it dry, and you get a dark ring with a pale middle, not an even stain. The pigment started out spread through the whole drop. The drop's edge… Physics2 min read Why a tossed tennis racket flips: the intermediate axis theorem Spin a tennis racket about its handle or its face and it flies cleanly. Spin it about the third axis and it flips, even in orbit where nothing pushes on it… Physics3 min read Why water drops last longer on a hotter pan: the Leidenfrost effect Flick water onto a warm pan and it sizzles away in a second. Make the pan hotter, past about 193 °C, and something odd happens: the drop pulls into a bead… Physics5 min read