205, 206.]
§16. Illumination of the Eye and the Ophthalmoscope
239
bundle of rays proceeds from this point x to the pupil of the patient’s
eye. According to propositions I and II, some of this light must
return to the illuminating object, and some of it must go to the pupil
of the observer’s eye. Suppose P denotes the area of the pupil of the
patient’s eye, and p denotes the area of the cross section in this same
plane of that part of the bundle of rays which returns to the illuminat¬
ing object. Moreover, let H denote the brightness of illumination
that would exist at the given place on the retina if the patient looked
directly at the source of light and focused it on his retina. This magni¬
tude may be called the normal brightness of illumination. It depends
essentially on the structure of the retina itself, and, of course, also on
the brightness of the illuminating object and on the size (P) of the
pupil of the patient’s eye. When an ophthalmoscope is employed, the
actual brightness of illumination of this part of the retina is necessarily
less than this; that is, it is equal to
Now let Q denote the area of the pupil of the observer’s eye; and let q
denote the area of the cross section in this plane of the part of the
bundle of rays coming from x that enters the pupil of the observer’s
eye; then the brightness of this part of the retina as it looks to the
observer is
(b) Case when there is appreciable loss of light by reflection or
refraction. In all the types of ophthalmoscope hitherto constructed
the only one in which there is such a loss of light is in the case of the
construction proposed by the author where unsilvered glass plates are
used. In this case, and in all similar contrivances, the losses of the
bundle of rays going from the eye to the illuminating object are pre¬
cisely the same as those of the rays that actually go from the light to
the eye. Suppose that light of unit intensity proceeds from the source
to the illuminated eye, and produces there an illumination a ; and that
light of the same unit intensity proceeds from the patient’s eye to the
observer’s eye and produces there an intensity ß: then the above
expression has to be multiplied both by a and ß, so that it becomes:
a-ß-V-q
P'Q
H.
This complete reciprocity in the problem of the illumination of the eye as
contained in the preceding propositions has enabled us to investigate the
brightness of illumination of the images in every case by reducing the matter
to the determination of the procedure of a single bundle of rays. Otherwise,
the brightness at any particular place on the retina would have had to be found