Let c D be a biconvex lens, and A B an ob ject on one side of it, hut further removed than the focal point F. Every point of the object will send forth rays in all direc tions, but to avoid confusion, we will only consider those flowing from the extremities An. The rays emitted from A undergo re fraction, are altered in their direction, and are united at A' upon the secondary axes drawn from A through o, the centre of the lens. The rays from it are in like manner united at 13; consequently, A'n' is the image of the object AB, but inverted. Seen from the middle of the lens, the image and object appear at the same angle, for the angle is equal to the angle BG A, being angles at the vertex. The relative size of the object or the image depends upon the relative distance of each from the lens. If the object lie twice as far as the focal distance from the lens, the image will be formed on the other side at an equal distance, consequently the image and the object are equal in size. But if the object approach nearer to the glass, the image will recede, becoming larger. We thus obtain in verted and enlarged images of objects stand ing further from the lens than the focal dis tance, yet not so far as twice that distance. Thus the image A'B' is larger than the object AB. If the object be further removed from the glass than twice the focal distance, the image will be nearer ; we therefore obtain in verted diminished images of distant objects.
Dioptric phenonzena.—Krause has described the anterior surface of the cornea as being spherical, the posterior parabolic. We re cently had an opportunity of examining a human cornea in less than an hour after theeye had been extirpated from the living subject, and satisfied ourselves that, in that case at least, the two surfaces were perfectly parallel. According to Chossat the figure of the cornea is an ellipsoid of revolution about the major axis, which axis determines the axis of the eye. The ratio of the semi•axis of this ellipse to the excentricity he determines at P3 ; and this being nearly the same with the index of refraction, parallel rays incident on the cornea in the direction of its axis will be made to converge, with great exactness, to a focus si tuated behind it, the aberration, which would have existed had the external surface been of a spherical figure, being almost completely destroyed. The form of the crystalline lens is that of a solid of revolution, having its anterior surface much less curved than its posterior : by some authorities both surfaces are described as being ellipsoids of revolution about their lesser axes ; but Krause found the posterior surface • to have a parabolic curve, whose parameter was from 31"-' to 5"/. He found also that the elliptical curve of the an terior surface of the lens varied as regards its long axis, in different cases from 4"' to 5A. "; its short axis also varying from II"' to 2r. Dr. Albert de Grhefe informs us that he has repeated these observations, and ascertained them to be correct. Valee states that he has found by a comparison of Krauss's measure ments of the dimensions of the eye, that the exterior convex surfaces have exactly that geometrical form which produces foci free from deviations. He calls them optoidal sur
faces, and also finds that the posterior convex surfaces are at least so far optoidal, as the pencils of light penetrating into the eye in fringe upon them. The axes of the two sur faces of the lens are not exactly coincident in direction with each other, nor with that of the cornea.
The refractive index of the surface of the lens is, according to 1.3767 ; of the centre P3990, the mean being that of the vitreous humour is P3394; thus the refractive density of the lens being greater than that of either the aqueous or vitreous humour, it exercises an important influence on the converging rays incident on it from the cornea. The effect of its elliptic figure is probtibly to correct the aberration .of ob lique pencils, and general aberration is still further obviated by the peculiar and varying density of its substance. By Professor James Forbes the variable- density is supposed to alter the figure of the lens under pressure, and so to assist in focal adjustment.
As the rays refracted by the aqueous hu mour pass into the crystalline, and those from the crystalline into the vitreous humour, the indices of refraction of the separating sur face of these humours will be, according to Brewster : From aqueous humour to outer layer of crystalline - - - - PO466, From ditto to crystalline, using the mean index - - - - 1.0353 From vitreous to crystalline outer layer - - - - - 1.0445 From ditto to ditto, using the mean • index - - - P0332 Suppose, then, the eye to be directed to wards an object, the rays of light proceeding from that object are thus disposed of. Those which strike the cornea very obliquely are reflected, as are those which impinge upon the sclerotic ; a large proportion of the rays, however, pass through the cornea, being power fully refracted by it, and the aqueous mem brane, and less by the aqueous behind : proceeding onwards, many of the rays are arrested by the iris, some being ab sorbed, others reflected, conveying the colours and brilliancy characteristic of that membrane. The more central rays pass through the pupil and the crystalline lens. The layers of this body, increasing in density from the circum ference to the centre, resemble in their effect upon the rays the atmosphere of this earth, which causes a gradual bending of the rays flowing from the heavenly bodies ; so the crys talline lens by its form and structure gradually but powerfully increases the convergence of the rays which penetrate it, both on their entrance and their exit. They then traverse the vitreous humour, — the chief use of which appears to be to afford support to the expanded retina, —and are brought in a perfectly natural eye, to foci upon the retina, forming there an exact but inverted picture of the object. If the eye of a white rabbit or any other albino be carefully cleansed, the flame of a taper held before the cornea may be seen inverted at the back of the eye, increasing in size as the taper is brought near, diminishing if it retires, and ever moving in the direction opposite to that given to the flame.