A lifeguard is on the sand and sees someone drowning in the sea, further out and off to one side. Which path should the lifeguard take? The straight line is the shortest path but not the fastest: running on sand is much quicker than swimming. It pays to run a bit further along the beach so as to swim less. Fermat realized that light makes exactly this choice. Reflection: the shortest path The oldest idea concerns mirrors. In the 1st century, Heron of Alexandria had already noticed that light, when reflected, follows the shortest path between two points by way of the mirror.
In Newton’s time it was already known that a glass prism, with sunlight passing through it, produces a coloured band. The accepted explanation came from Aristotle and Descartes: white light is pure, and the glass modifies it, darkening it little by little. A small modification gave red; a large one, blue and violet. Newton had his doubts. What if the colours were already inside white light, and the prism merely separated them?