Images in convex mirrors and their diminution with distance
Optics of the simulacrum on a convex mirror, proven by the perspective of painting
Two columns of optical reasoning, each accompanied by a figure of converging rays labelled with letters. Leonardo argues that the image (simulacro) is carried the smaller onto a convex mirror the more remote the object is: with mirror h i and image b c cut at cathetus S t, moving the object to o p shrinks its cut. He qualifies that among objects of equal size the image grows smaller with distance but never truly smaller in proportion to the mirror, appealing to the perspective of painting for proof. The left column notes that at great distance the image can even remain larger than the mirror that receives it.
On this page
The image diminishes on a convex mirror with distance
Every image is carried the smaller onto convex mirrors the more remote the object is. With h i the convex mirror and b c the image at a given distance, its cathetus is cut at S t; moving the object b c to o p makes its cathetus smaller in its cut upon the mirror within S t.
Proof by the perspective of painting
Among things of equal size the image shows smaller on the more distant convex mirror, yet in truth never smaller in proportion. This is proven by the perspective of painting: with the eye at the first object and then at an equal second object farther off, the image is smaller in itself but not smaller relative to the mirror where it is imprinted.
The mirror body shrinks faster than the image
The body of the mirror diminishes more at o p, in proportion to the image, than it does at n m; and one could move so far away that the image would remain larger than the mirror that receives it.