It is evident, therefore, that the minimum number of sides, i.e., the bounding faces, exclusive of the ends, which a prism can have is three. In this form, it constitutes a most valuable instrument of research in physical optics. A convex lens is practically merely a curved form of two prisms combined, their bases being brought into contact; on the other hand the concave lens is simply a reversal of the position of the apices brought into contact, as shown in [Fig. 11]. Both convex and concave lenses are therefore closely related to the prism.
Reflection.—The laws that govern the change of direction which a ray of light experiences when it strikes upon the surfaces of separation of two media and is thrown back into the same medium from which it approached is as follows:—When the reflecting surface is plain the direction of the reflected ray makes with the normal to the surface the same angle which the incident ray makes with the same normal; or, as it is usually expressed, the angles of reflection and incidence are equal. When the surfaces are curved the same law holds good. In all cases of reflection the energy of the ray is diminished, so that reflection must always be accompanied by absorption. The latter probably precedes the former. Most bodies are visible by light reflected from their surfaces, but before this takes place the light has undergone a modification, namely, that which imparts colour peculiar to the bodies viewed. When light impinges upon the surface of a denser medium part is reflected, part absorbed, and part refracted. But for a certain angle depending upon the refractive index of the refracting medium no refraction takes place. This angle is termed the angle of total reflection, since all the light which is not absorbed is wholly reflected.
Multiple images are produced by a transparent parallel plate of glass. If the glass be silvered at the back, as it usually is in the microscope-mirror, the second image is brighter than the first, but as the angle of incidence increases the first image gains upon the second; and if the luminous object be a lamp or candle, a number of images, one behind the other, will be visible to an eye properly placed in front. This is due to the fact that the reflecting power of a surface of glass increases with the angle of incidence.
Fig. 7.—Conjugate Foci of Curved Surfaces.
Concave Surfaces.—Rays of light proceeding from any given point in front of a concave spherical mirror, are reflected so as to meet in another point, and the line joining the two points passes through the centre of the sphere. The relation between them is or should be mutual, hence they are termed conjugate foci. By a focus in general is meant a point in which a number of rays of light meet, and the rays which thus meet, taken collectively, are termed a pencil. [Fig. 7] represents two pencils of rays whose foci, S s, are conjugate, so that, if either of them be regarded as an incident pencil, the other will be the corresponding reflected pencil. Each point, in fact, sends a pencil of rays which converge, after reflection, to the conjugate focus. The principal focal distance is half the radius of curvature. But it will not escape attention that concave mirrors have two reflecting surfaces, a front and a back. This, however, does not practically disturb its virtual focus, since the achromatic condenser when brought into use collects and concentrates the light received from the mirror upon an object for the purpose of rendering it more distinctly visible to the eye when viewing an object placed on the stage of the microscope. The images seen in a plane mirror are always virtual, and any spherical mirror, whether concave or convex, is nearly equivalent to a plane mirror when the distance of the object from its surface is small in comparison with the radius of curvature.
Lenses.
Forms of Lenses.—A lens is a portion of a refracting medium bounded by two surfaces which are portions of spheres, having a common axis, termed the axis of the lens. Lenses are distinguished by different names, according to the nature of their surfaces.
Fig. 8.—Converging and Diverging Lenses.