This section is from the book "Telephotography: An Elementary Treatise On The Construction And Application Of The Telephotographic Lens", by Thomas Rudolphus Dallmeyer. Also available from Amazon: Telephotography and Telephotographic Lens.
The laws of reflection and refraction of light at plane and spherical surfaces are contained in every elementary treatise on "Optics."* The reader will do wisely to master them, although an intimate knowledge of the subject is not necessary in order to understand how images are formed by lenses and combinations of lenses.
For our present purpose, it will only be necessary to understand how pencils of light are affected in their passage through a lens, and to define certain characteristics, or elements as they are termed, of the lens itself.
When a ray of light passes from one transparent homogeneous medium into another (either denser or rarer), it continues its course in a straight line when it meets the surface of the medium perpendicularly (or at "right angles," as it is termed), as a, b, c, d. (Fig. n.) If the ray encounters the second medium in a slanting (oblique) direction, or at any other angle than a right angle, taking a direction a' b', it alters its direction in passing through the second medium, and is bent, or "refracted," as at b'c', continuing its altered course in a straight line within the second medium. On passing from a second into a third medium, the same process continues as at c' d', and so on. (See Notes.)
The altered direction of the ray will depend upon the character of the medium which it meets in its original course. If the second medium is denser (or more refractive) than the first, the ray is bent towards the perpendicular p p drawn through the point where it meets the second surface as at b' c'. If, on the other hand, the ray is pursuing its course in a straight line in a denser medium b' d than that which it next encounters, it is bent away from the perpendicular p' p' drawn through this point as at c'd'. If one medium be denser (or have a higher refractive index, as it is termed) than another, the more will it bend or refract a ray meeting it at a given obliquity.
* Cole's " Photographic Optics " (Sampson Low & Co.).
In Fig.11 we have illustrated the passage of a ray of light through a plane plate of glass with parallel faces, and it will be observed that after passing through the glass it emerges in a direction parallel to its original direction. If a'b' had not encountered a medium of different density, it would have pursued the course a' b' c" d". The effect of the slab of glass with parallel sides has been to divert the ray of light from its course, but not to alter its direction. If the glass is very thick, as in the figure, the ray is considerably diverted ; if it be very thin, it is easy to see that its course is very little affected, but in neither case is the direction altered. We shall see presently that certain rays pass through a lens in precisely the same manner, and shall make use of these rays in our investigations on account of the simplicity of the conditions. It must be noted that the ray originates in one medium (air), and after refraction by the denser medium (glass) emerges again into the same medium (air). This is necessary for the condition; for if the last medium were different from the first, the condition of parallelism would not hold good. In photography the first and final media (air) are almost invariably the same ; an exception would occur if we placed the outside surface of the lens under water to photograph fish, etc.
A lens is a portion of a refracting medium bounded by two spherical surfaces of revolution which have a common axis, called the axis of the lens.
With o as a centre and radius o r describe the curve of the spherical surface of revolution r a' r ; similarly with o' as centre and radius o' r' describe the curve of the spherical surface of revolution r' a r'. The portion l represents the section of a lens, o and o' are the two centres of curvature of the surfaces ; o o', the line joining them, is the axis of the lens ; o r, o' r' the radii; a, a', the points where the surfaces cut the axis, are called the poles, and the distance between these bounding surfaces, or poles, a a', the thickness of the lens. The surfaces of revolution are either spherical or plane - a plane surface being, of course, a particular case of a spherical surface where the radius is infinitely great.
Lenses are classified according to their forms. A lens bounded (1)by two convex surfaces is called a double-convex lens; (2) by a convex surface and a plane surface, zconvexo-plane, or plano-convex lens, according to the surface presented to the light; (3) by a convex surface and a concave surface, a convexo-concave or concavo-convex lens, according to the surface presented to the light. A lens of this last form is also termed a meniscus.
(4) Similarly, a lens bounded by two concave surfaces is called a double-concave lens; (5) by a plane surface and a concave surface, a plano-concave, or concavo-plane lens, according to the surface presented to the light; (6) by a concave surface and a convex surface, a concavoconvex or convexo-concave lens, according to the surface presented to the light. This form of lens is also called a meniscus.
Convex Or Positive Lenses. Concave Or Negative Lenses.
The first three forms of lenses are thicker in the centre than the edge and are called convex or positive lenses, and are capable of forming real images. The last three forms of lenses are thinner in the centre than the edge, and are called concave or negative lenses ; they cannot form real images when used alone, but form imaginary or virtual images. We may add here, for a special reason that will afterwards be made clear, that we may conceive a "lens" having two plane surfaces; this lens can be imagined to form an image at infinity.