The optical constants of the human eye may be still further
simplified by assuming that the two principal points and the two
nodal points respectively are identical. Thus we may construct
a reduced eye, in which the principal point is 2.3448 mm. behind the
cornea and the single nodal point is 1.4764 mm. in front of the
posterior surface of the lens. The refracting surface, or lens, has a
radius of 5 mm. and is 3 mm. behind the cornea; and the index
of refraction is that of the aqueous humour, or 10377, or 1.3379.
Fig. 2.—Transverse Section of an Ideal or Schematique Eye.
A, summit of cornea; SC, sclerotic; S, Schlemm's canal; CH, choroid; I, iris; M, ciliary muscle; R, retina; N, optic nerve; HA, aqueous humour; L, crystalline lens, the anterior of the double lines on its face showing its form during accommodation; HV, vitreous humour; DN, internal rectus muscle; DE, external rectus; YY′, principal optical axis; ΦΦ, visual axis, making an angle of 5° with the optical axis; C, centre of the ocular globe. The cardinal points of Listing: H₁H₂, principal points; K₁K₂, nodal points; F₁F₂, principal focal points. The dioptric constants according to Giraud-Teulon: H, principal points united; Φ₁Φ₂, principal foci during the repose of accommodation; Φ′₁Φ′₂, principal foci during the maximum of accommodation; O, fused nodal points.
2. The Formation of an Image on the Retina.—This may
be well illustrated with the aid of a photographic camera.
If properly focused, an inverted image will be seen on the
glass plate at the back of the camera. It may also be observed
by bringing the eyeball of a rabbit near a candle flame. The
action of a lens in forming an inverted image is illustrated by
fig. 3, where the pencil of rays proceeding from a is brought
Fig. 3.—Inversion by Action of a Lens.
to a focus at a′,
and those from
b at b′;
consequently the image
of ab is inverted
as at b′a′. The
three characteristic
features of
the retinal image are: (1) it is reversed; (2) it is sharp and
well defined if it be accurately focused on the retina; and
(3) its size depends on the visual angle. If we look at a distant
object, say a star, the rays reaching the eye are parallel, and
in passing through the refractive media they are focused
at the posterior focal point—that is, on the retina. A line
from the luminous point on the retina passing through the
nodal point is called the line of direction. If the luminous
object be not nearer than, say, 60 yds. the image is still
brought to a focus on the retina without any effort on the
part of the eye. Within this distance, supposing the condition
of the eye to be the same as in looking at a star, the image
would be formed somewhat behind the posterior focal point,
and the effect would be an indistinct impression on the retina.
To obviate this, for near distances, accommodation, so as to
adapt the eye, is effected by a mechanism to be afterwards
described.
Fig. 4.—Formation of Circles of Diffusion.
When rays, reflected from an object or coming from a luminous point, are not brought to an accurate focus on the retina, the image is not distinct in consequence of the formation of circles of diffusion, the production of which will be rendered evident by fig. 4. From the point A luminous rays enter the eye in the form of a cone, the kind of which will depend on the pupil. Thus it may be circular, or oval, or even triangular. If the pencil is focused in front of the retina, as at d, or behind it as at f, or, in other words, if the retina, in place of being at F, be in the positions G or H, there will be a luminous circle or a luminous triangular space, and many elements of the retina will be affected. The size of these diffusion circles depends on the distance from the retina of the point where the rays are focused: the greater the distance, the more extended will be the diffusion circle. Its size will also be affected by the greater or less diameter of the pupil. Circles of diffusion may be studied by the following experiment, called the experiment of Scheiner:—
Fig. 5.—Diagram illustrating the Experiment of Scheiner.
Let C be a lens, and DEF be screens placed behind it. Hold in front of the lens a card perforated by two holes A and B, and allow rays from a luminous point a to pass through these holes. The point o on the screen E will be the focus of the rays emanating from a; if a were removed farther from the lens, the focus would be on F, and if it were brought near to C, the focus would then be on D. The screens F and D show two images on the point a. If, then, we close the upper opening in AB, the upper image m on F and the lower image n on D disappear. Suppose now that the retina be substituted for the screens D and F, the contrary will take place, in consequence of the reversal of the retinal image. If the eye be placed at o, only one image will be seen; but if it be placed either in the plane of F or D, then two images will be seen, as at mm, or nn; consequently, in either of these planes there will be circles of diffusion and indistinctness, and only in the plane E will there be sharp definition of the image.
To understand the formation of an image on the retina,
suppose a line drawn from each of its two extremities to the
nodal point and continued onwards to the retina, as in fig. 6,
where the visual angle is x. It is evident that its size will
Fig. 6.—The Visual Angle.
depend on the size of the
object and the distance of the
object from the eye. Thus,
also, objects of different sizes,
c, d, e in fig. 6, may be
included in the same visual
angle, as they are at different
distances from the eye. The
size of the retinal image may
be calculated if we know the
size of the object, its distance
from the nodal point o,
and the distance of the nodal
point from the posterior focus.
Let A be the size of the object, B its distance from the
nodal point, and C the distance of o from the retina,
or 15 mm.; then the size of the retinal image x = (A + 15)/B.
The smallest visual angle in which two distinct points
may be observed is 60 seconds; below this, the two sensations
fuse into one; and the size of the retinal image
