If the body upon the surface of which the rays are incident be transparent, some of the rays will be refracted and will pass through it, whilst others will be reflected. The proportion of those reflected is smallest when the rays are incident perpendicularly to the surface; but this increases as the incident rays become more oblique, i. e. as the angle of incidence becomes greater, although at no degree of obliquity are the whole of the rays reflected. The case is different, however, with those rays which enter the substance and impinge upon its inner or second surface; for these at a particular angle of incidence undergo total reflexion, so that none of the rays are transmitted at the second surface. The angle of total reflexion is constant for the same medium, but different for different media: thus in crown glass it is equal to about 40°, in flint-glass 38°, &c.; and this internal reflexion from the second surface of transparent media is more perfect than that occurring at the surface of opake reflecting surfaces or mirrors.
If the reflecting surface be concave, as in [Pl. XII.] fig. 4, parallel rays will be reflected to a focus a, nearer the mirror than the centre of its curvature b, and this focus is called the principal focus; while diverging rays are brought to a focus nearer the centre of curvature; and converging rays form a focus further from the centre of curvature.
Lenses.—In most instances, as far as the microscope is concerned, the surfaces of the glass through which the rays of light are transmitted are not plane or flat, but curved-being either convex or concave, and belonging to convex or concave lenses. In considering the course of rays through curved surfaces, the refraction may be viewed as taking place at a plane surface forming a tangent at the point of incidence of each ray; or each curved surface may be regarded as consisting of a number of minute plane surfaces placed at right angles to the perpendicular. Thus, in [Pl. XII.] fig. 5, the ray a, incident at the point b of the curved surface, is refracted towards the perpendicular p, as if it had fallen upon the plane surface represented by the tangent t. The forms of the most common lenses are represented in [Pl. XII.] figs. 6-10;—fig. 6 being doubly convex, or both surfaces being convex; fig. 7, plano-convex, or one surface plane, the other convex; fig. 8, doubly concave, or both surfaces being concave; fig. 9, plano-concave, one surface being plane, the other concave; and fig. 10 is a meniscus, in which one surface is convex and the other concave. The curved surfaces of lenses are usually portions of spheres.
The manner in which the course of a ray may be traced through a lens is illustrated by [Pl. I.] fig. 11, which requires no explanation after what has been already stated.
To facilitate the comprehension of the general action of lenses, they may be regarded as composed of two triangular prisms, with their bases in contact in a convex lens, as in fig. 12; their apices being opposed in a concave lens, as in fig. 13.
The point to which the rays converge after passing through a convex lens is called the focus ([Pl. XII.] fig. 14 f), the distance of which from the centre of the lens, called the focal length, obviously depends upon the direction of the incident rays. When these are parallel, which those coming from distant objects may be considered to be, the focus at which they meet is called the principal focus, or the focus for parallel rays: thus, in [Pl. XII.] fig. 14, the parallel rays meet at f, which is the principal focus.
If the incident rays are convergent, as in [Pl. XII.] fig. 15, the focus o will be situated nearer the lens than the principal focus, f. If, on the other hand, they are divergent, as in [Pl. XII.] fig. 16, the focus f will be situated further from the lens than the principal focus o. By concave lenses the incident rays are rendered divergent, as in [Pl. XII.] fig. 17, as if they emanated from a point f, situated on the same side of the lens as that upon which the rays are incident, and called the virtual focus.
Spherical aberration.—Although, as a general expression, we have stated that the rays of light meet at a focus on passing through a convex lens, this is not strictly correct. For, in ordinary convex lenses, the marginal rays are more refracted than the central ones, and meet at focal points nearer the lens than the latter, as shown in Pl. XII. fig. 18. This important defect is called spherical aberration, and arises from the lateral rays being incident upon more oblique portions of the curved surface of the lens than the central rays. Hence objects seen through such lenses appear misty and confused, the central and lateral parts of a flat object not being visible at the same time; and even when the marginal parts are visible, they appear distorted or deformed.
Spherical aberration is greatest in the most convex lenses; and, in a plano-convex lens, it is least when parallel rays enter at or emerge from its convex surface.
In certain lenses, the convex surface of which has the form of a parabola, a hyperbola, or an ellipse, the spherical aberration is absent; but it is impossible to grind microscopic lenses of these forms with absolute accuracy, so that the fact is of no practical value.