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.
Light consists of vibrations of a highly elastic solid medium termed ether, which pervades all space. These vibrations are conveyed to the brain by means of our eyes, and produce the sensation of sight.
All visible objects surrounding us are sources of light. These sources are either self-luminous bodies, such as the sun, fixed stars, electric light, and bodies in a state of combustion; or illuminated bodies, as the moon, planets, or any body that can be seen by light borrowed from a self-luminous body.
For our present purpose, it is not necessary to distinguish these two classes of objects; every point in every object is a source of light.
Medium. - Any space through which light can pass is called a medium; a vacuum, air, gases, water, glass, etc, are media. Bodies through which light can pass are termed transparent, while those through which it cannot pass are termed opaque.
Light travels in straight lines with uniform velocity in any homogeneous medium. In the practice of photography, particularly in Telephotography, we are occasionally reminded of the converse of this law. In observing a distant object across an open landscape, or a ship at sea, the object under observation sometimes appears to be disturbed and unsteady, owing to a kind of "boiling" appearance of the atmosphere, which is not homogeneous for the time being. When the atmosphere is in this condition, it is hopeless to expect to obtain well-defined photographic images. The observations of astronomers in this country are frequently disturbed by the lack of homogeneity in the atmosphere, even on apparently the clearest nights.
Light consists of separable and independent Parts. - If we place an opaque object in the light proceeding from a luminous body, a portion of the light is intercepted, but the rest of the light proceeds to illuminate surfaces upon which it falls, neither adding to nor diminishing the illumination. Again, light from two independent sources may travel along the same path without interference. Hence light is capable of quantitative measurement; that is to say, we can compare the intensity of two given sources of light, or in general measure the intensity of light in terms of some fixed standard. In photographic practice, we measure the intensity of light by an instrument known as an "actinometer," the action of which is based upon the period of time taken by the light to discolour a photographically active material to a given shade; the greater the intensity of the light (photographically), the shorter the period of time taken to discolour the sensitive material.
Absorption and Transmission of Light. - When light travels through any homogeneous medium, part is absorbed and only part transmitted. We shall neglect absorption entirely and presume that all media are perfectly transparent.
Reflexion of Light on passing from one Medium to another. - When light passes from one homogeneous medium to another, part is reflected at the surface of the second medium, and part transmitted. In the construction of photographic instruments, we consider the whole of the light to be transmitted. In our study of the theory of the Telephoto-graphic lens, we shall not then take these factors into consideration; but, in practice, it must be borne in mind that the absorption of light by thick lenses, and the loss of light by reflexions are not in reality quite negligible quantities. Greater optical perfection in an instrument is frequently attained, however, by both these means as exemplified in some of the most recent advances in photographic lens construction.
A Ray of Light. - For theoretical considerations, it is often convenient to consider a portion of light travelling along some particular line in a medium, quite apart from the remainder. We may think of it as an indefinitely attenuated slender cone, or, as older writers put it, the least portion of light we can conceive to exist independently. We term such a portion of light a Ray of Light.
A Pencil of Rays is a collection of rays which never deviate far from some central fixed ray, which is called the axis of the pencil. If the pencil proceeds towards a point, it is termed a convergent pencil; if, on the other hand, it proceeds from a point, it is termed a divergent pencil.
Focus. - If a pencil of rays meets in a point, that point is called the focus. A focus is not a measurement, but a position.
Parallel Rays. - The form of a pencil of rays is considered as that of a right cone. The limiting form of a cone when the vertical angle is indefinitely small is a cylinder. Such a cylindrical pencil of rays is termed parallel.
The intensity of light at different distances from a luminous point is inversely as the square of the distance.
As we know that light travels in straight lines in all directions, it is easy to find the alteration in the intensity of the illumination* of a surface by changing its distance from the source of light.
* It is thought unnecessary to introduce " units " into this popular explanation.
If l be a luminous point, and we imagine concentric spheres with radii r r', etc, described about it, the total quantity of light received by the surface of the sphere of radius R l is the same as that which would reach the surface of the sphere of radius r' l. Now, as the surfaces of the spheres are in direct ratio of the square of their radii, the quantity of light which falls on a given extent of surface must be inversely in the same ratio.
In the same manner, if we place a small plane surface at a at a given distance from l, the whole quantity of light received at a would be distributed over b, c, and d placed at distances 2, 3, and 4 times the distance of a from the light. The areas of b, c, and d are 4, 9, and 16 times as great as a, or the intensity of the light on the unit of surface is inversely as the square of the distance from the source of illumination. This law is termed the "law of inverse squares," and it has a very important bearing upon our present subject.
The illumination of the areas we have just discussed is taken as perpendicular to the incident light.
The illumination of an area inclined to the incident light is found by multiplying the former by the cosine of the angle of incidence. This law, together with the law of inverse squares, enables us to measure the falling off of the illumination from the centre towards the edge of a photographic plate, but need not be dwelt upon here.