corresponding to this angle is .004 mm., nearly the diameter of a single retinal rod or cone. Two objects, therefore, included in a visual angle of less than 60 seconds, appear as one point. A small visual angle is in most eyes a condition of sharpness of definition. With a large angle, objects appear less sharply marked. Acuteness is determined by a few retinal elements, or even only one, being affected. A very minute image, if thrown on a single retinal element, is apparently sufficient to excite it. Thus it is possible to see a brilliant point in an angle even so small as ¼ of a second, and a sharp eye can see a body the 150th of a line in diameter—that is, about the 1600th part of an inch.
3. The Optical Defects of the Eye.—As an optical instrument, the eye is defective; but from habit, and want of attention, its defects are not appreciated, and consequently they have little or no influence on our sensations. These defects are chiefly of two kinds—(1) those due to the curvature of the refractive surfaces, and (2) those due to the dispersion of light by the refractive media.
(a) Aberration of Sphericity.—Suppose, as in fig. 7, M A K
Fig. 7.—Spherical Aberration.
to be a refractive
surface on which
parallel rays from
L to S impinge, it
will be seen that
those rays passing
near the circumference
are brought to
a focus at F¹, and
those passing near
the centre at
F²—intermediate rays
being focused at N. Thus on the portion of the axis
between F¹ and F² there will be a series of focal points,
and the effect will be a blurred and bent image. In the eye
this defect is to a large extent corrected by the following
arrangements: (1) the iris cuts off the outer and more
strongly refracted rays; (2) the curvature of the cornea is
more ellipsoidal than spherical, and consequently those
farthest from the axis are least deviated; (3) the anterior
and posterior curvatures of the lens are such that the
one corrects, to a certain extent, the action of the other;
and (4) the structure of the lens is such that its power of
refraction diminishes from the centre to the circumference, and
consequently the rays farthest from the axis are less refracted.
(b) Astigmatism.—Another defect of the eye is due to different meridians having different degrees of curvature. This defect is known as astigmatism. It may be thus detected. Draw on a sheet of white paper a vertical and a horizontal line with ink, crossing at a right angle; at the point of distinct vision, it will be found impossible to see the lines with equal distinctness at the same time; to see the horizontal line distinctly the paper must be brought near the eye, and removed from it to see the vertical. In the cornea the vertical meridian has generally a shorter radius of curvature, and is consequently more refractive than the horizontal. The meridians of the lens may also vary; but, as a rule, the asymmetry of the cornea is greater than that of the lens. The optical explanation of the defect will be understood with the aid of fig. 8. Thus, suppose the vertical meridian C A D to be more strongly curved than the horizontal F A E, the rays which fall on C A D will be brought to a focus G, and those falling on F A E at B. If we divide the pencil of rays at successive points, G, H, I, K, B, by a section perpendicular to A B, the various forms it would present at these points are seen in the figures underneath, so that if the eye were placed at G, it would see a horizontal line a a′; if at H, an ellipse with the long axis a a′ parallel to A B; if at I, a circle; if at K, an ellipse, with the long axis, b c, at right angles to A B; and if at B, a vertical line b c. The degree of astigmatism is ascertained by measuring the difference of refraction in the two chief meridians; and the defect is corrected by the use of cylindrical glasses, the curvature of which, added to that of the minimum meridian, makes its focal length equal to that of the maximum meridian.
Fig. 8.—Diagram illustrating Astigmatism.
(c) Aberration of Refrangibility.—When a ray of white light
traverses on a lens, the different rays composing it, being
unequally refrangible, are dispersed: the violet rays (see fig. 9),
Fig. 9.—Diagram illustrating the Dispersion of
Light by a Lens.
the most refrangible,
are brought
to a focus at e,
and the red rays,
less refrangible,
at d. If a screen
were placed at e,
a series of
concentric coloured
circles would be formed, the central being of a violet, and
the circumference of a red colour. The reverse effect would
be produced if the screen were placed at d. Imagine the
retina in place of the screen in the two positions, the
sensational effects would be those just mentioned. Under ordinary
circumstances, the error of frangibility due to the optical
construction of the eye is not observed, as for vision at near
distances the interval between the focal point of the red and
violet rays is very small. If, however, we look at a candle flame
through a bit of cobalt blue glass, which transmits only the red
and blue rays, the flame may appear violet surrounded by blue,
or blue surrounded by violet, according as we have accommodated
the eye for different distances. Red surfaces always appear
nearer than violet surfaces situated in the same plane, because
the eye has to be accommodated more for the red than for the
violet, and consequently we imagine them to be nearer. Again,
if we contemplate red letters or designs on a violet ground the
eye soon becomes fatigued, and the designs may appear to move.
(d) Defects due to Opacities, &c., in the Transparent Media.—When small opaque particles exist in the transparent media, they may cast their shadow on the retina so as to give rise to images which are projected outwards by the mind into space, and thus appear to exist outside of the body. Such phenomena are termed entoptic. They may be of two kinds: (1) extra-retinal, that is, due to opaque or semi-transparent bodies in any of the refractive structures anterior to the retina, and presenting the appearance of drops, striae, lines, twisted bodies, forms of grotesque shape, or minute black dots dancing before the eye; and (2) intra-retinal, due to opacities, &c., in the layers of the retina, in front of Jacob's membrane. The intra-retinal may be produced in a normal eye in various ways. (1) Throw a strong beam of light on the edge of the sclerotic, and a curious branched figure will be seen, which is an image of the retinal vessels. The construction of these images, usually called Purkinje's figures, will be understood from fig. 10. Thus, in the figure to the left, the rays passing through the sclerotic at b″, in the direction b″ c, will throw a shadow of a vessel at c on the retina at b′, and this will appear as a dark line at B. If the light move from b″ to a″, the retinal shadow will move from b′ to a′, and the line in the field of vision will pass from B to A.
