The sun's image on water and the borrowed light of the stars
Notebook D: how pupil size, reflection and distance govern the apparent size of a light
Leonardo argues that the sun casts a single image across the whole sphere of a body of water, yet that image appears multiplied because each animal's eye sees it from its own position. He reasons that the smallness of the pupil is what shrinks the reflected sun to a tiny point, and calculates that a pupil 25 braccia across would see a sun-image spanning 78 and 4/7 braccia. Extending the idea to the sky, he concludes that the stars, though many times larger than the earth, only look tiny because of their distance, and that their light is not their own but the sun mirrored in their surfaces as in water. The page is dense mirror-script in a main column with short marginal notes at right.
On this page
One sun, seemingly many reflections
The reflected sun is a single image over the whole watery sphere that both sees and is seen by the sun, but it seems split into as many parts as there are eyes looking at the water. Sailors carried across the world all see the sun's image at once in every water of their hemisphere, from every position and motion.
Pupil size sets the span of the sun's image
Walking about 25 braccia along a bridge makes the sun's image slide across the river; gathering all those images gives a fiery beam. If a pupil were 25 braccia in diameter it would, without moving, see a sun-image spanning 78 braccia and 4/7. The tiny real pupil is why the reflected sun looks minute.
Distance shrinks even the greatest body to a point
If the eye were far enough from the sphere of water that the whole sphere diminished, in perspective, to the size of an ordinary sun-image, then the entire lit sphere would read as a single image of the sun. Remote things, however vast, are shown of the smallest figure.
Stars shine with reflected sunlight
Raising the eyes to the starry sky reveals stars many times larger than the earth that distance makes tiny. Their light is not their own power but a single image of the sun mirrored in them; of themselves they have no light, only a surface, like the sphere of water, fit to receive and return the sun's light.
