Lenses and Waves

28 CHAPTER 2
the book. In the same way, he argued, all the points of the sun project
overlapping images of the aperture (Figure 14). The resulting image has the
shape of the sun, albeit with a blurred edge. In the projection of an eclipse,
the image of the shadow of the moon is partially overlapped by the image of
the sun. Consequently, the diameter of the moon seems too small. In chapter
two of Paralipomena, Kepler had solved the apparent anomaly of pinhole
observations in principle, building on the previous chapter, he elaborated the
exact solution in the eleventh and final chapter.
Image formation
Kepler came to the conclusion that there were more problems in
perspectiva, in particular its core, the theory of vision. In chapter five of
Paralipomena, he elaborated a new theory of vision on the basis of his newly
gained understanding of image formation. In its fourth section, Kepler listed
the defects of existing theories of vision, the most important being a wrong
understanding of the anatomy of the eye and of the mathematics of image
formation. Perspectivist theories considered the lens the sensitive organ of
the eye, whereas recent anatomical investigations had demonstrated,
convincingly according to Kepler, that the retina receives images from
objects. He himself had shown the defects of the perspectivist understanding
of image formation, calling Witelo by name, and he now went on to
reconsider the optics of the eye.
In perspectivist theory, each point of an object emits rays of light in each
direction. This, however, raises the problem how a sharp image can be
perceived, that is: how a one-to-one relationship between a point of the
object and a point of the image in the eye is established. According to
Alhacen there can be only one point in the eye where a ray from a point of
the object can be perceived. He stated that this must be the one entering the
eye perpendicularly (and thus perpendicular to the lens). He explained that
the other rays are refracted by the eye, therefore weakened, and thus do not
partake in the formation of the image. 61 In medieval optics, images were
therefore taken to be produced by single rays from each point of the object.
Kepler saw no reason to differentiate between weak and strong rays. He did
not see, for that matter, why refraction would weaken a ray. In his view, all
rays emitted by a point should somehow partake in the formation of an
image. In the case of pinholes this resulted in a fuzzy image, but what about
the sharp images by which we generally see the world?
Kepler’s answer was that the cone of rays coming from one point is
somehow brought to focus on the retina. Following certain recent
anatomical observations he considered the retina as the sensitive organ of
the eye, in contrast to perspectivist theory that had assigned the power of
visual perception to the crystalline humor. According to Kepler, the various
humors of the eye can be regarded as one refracting sphere. In the fifth
61 Alhacen, Optics I, 68 (book 1, section 17) and 77 (book 1, section 46).