Optics of the eye: vision, the pupil and lit spheres
The 4x rule of visual size, a proof that sight is not a single point, and how a luminous body lights an opaque sphere.
Five notes and their diagrams treat the geometry of vision and illumination. Leonardo gives a rule that a body larger than the space between the pupils must stand at least four times its own size away to be judged, and argues that the eye's perspective does not reduce to a single point, since the whole pupil sees and a small near object cannot hide a distant one; the same demonstration confirms that images enter the eye upside down. Two further notes and figures treat the lighting of an opaque sphere: why a luminous source cannot light the middle of the sphere, shown through the angles a d b and b c f on the central line b n, and how the amount illuminated depends on the relative size and distance of the luminous and shadowed bodies.
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The four-times rule for judging a body's size
Every body larger than the interpupillary space that must be judged by the eye will be at least four times its own size distant. If it is smaller than that interval of light, nothing nearer is comprehended by the eye unless four times the interval of the pupils is set between the eye and the thing seen. The accompanying figure of rays is lettered a and b.
Sight is not a point; images enter inverted
With the pupil taken as o p and the perspectivists' imagined point as n, Leonardo shows that a thing f smaller than the pupil cannot occupy the place b c, because the whole pupil sees: the half o n sees all of b e while the other half sees a c. Drawing lines o e and n b over the obstruction f proves the point, and confirms that all the species of objects enter the eye upside down, b above answering below at n e and the lower part above at o.
A luminous body cannot light the middle of a sphere
It is impossible, at any distance, for a luminous body to illuminate the middle of an opaque spherical body. The figure shows why the angles a d b and b c f cannot be equal upon the central line b n.
How size and distance govern the amount lit
The nearer a luminous body larger than the shadowed one comes, the more it lights it; but a luminous body smaller than the shadowed one lights it less as it nears and more as it withdraws. If the larger luminous body is moved away, the total illuminated always diminishes down toward the middle.
