The Medium Between Eye and Object: Refraction in Crystal
How a transparent medium of parallel surfaces displaces what lies behind it
A chapter of the Treatise on Painting on the nature of the medium interposed between eye and object, distinguishing media that have their own surface (water, crystal, other transparent things) from air, which has no continuous surface of its own. Leonardo argues that a medium bounded by a common surface never shows the object behind it in its true position. A lettered diagram proves the point with a crystal of parallel surfaces o r, through which the eye a sees the upper half of an object refracted (enlarged) while the lower half, seen through the air beneath, keeps its true place.
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Two kinds of interposed medium
The medium between the eye and the object is of two qualities: either it has a surface, like water and crystal or other transparent things, or it is without a common surface, like the air. The air rests upon the surfaces of the bodies enclosed within it and has no continuous surface of its own except at its lower and upper limit.
Refraction through the crystal of parallel surfaces o r
The eye a sees the half of the object n g behind it: the portion n m through the crystal b o, and the remainder m g through the air beneath the crystal. The line of the upper part n m bends at the entry of the crystal to make the line n b a, so that half of the object grows within the crystal b o while the other half diminishes in the air beneath at o p.
Why a medium never shows the object in its true place
A medium surrounded by a common surface never renders to the eye the object lying behind it in its true position. This optical rule underlies the painter's understanding of how transparent bodies shift the apparent location of what is seen through them.