This section is from the book "Complete Self-Instructing Library Of Practical Photography", by J. B. Schriever. Also available from Amazon: Complete Self-Instructing Library Of Practical Photography.
Circle Of Illumination. The aperture of the lens being circular, the rays of light passing out from the lens form a cone of light, and the field of the lens is therefore circular. A cross section through this cone at right angles to the axis of the lens will be a disc of light, smaller or larger as the section is taken nearer to or farther from the lens. This disc is the circle of illumination. If we take the cross section at the equivalent focal distance (see paragraph No. 608) from the lens, the disc is the circle of illumination at that distance. It is also referred to as the image circle, because the area of the disc is also the area of the field - the surface on which the image is formed - and when the diameter of image circle or circle of illumination is referred to in lens makers' catalogues, it means the diameter of the field at the distance of the equivalent focus.
Angle Of Field. The angle of field is the angle included between the lines drawn from opposite ends of the diameter to a certain point in the lens (the node of emission). For our purpose it will be sufficient to imagine the two lines drawn to the center of the diaphragm opening in a doublet lens. As this angle is narrower or wider, the lens is relatively a narrow angle or a wide angle lens.
Angle Of View. Angle of view is differently given - sometimes on the longer side of the plate and sometimes on the diagonal (a straight line joining two opposite corners). In the former case it is included between the lines drawn from the opposite ends of the plate, in the latter case between the lines drawn from the two opposite corners, to the same point in the lens. If the two lines, after crossing each other, are continued through and out in front of the lens, the amount of view included between them will be the amount included on the plate, either from end to end or from corner to corner.
Wide-Angle Lens. The term "wide-angle lens" is very often popularly misunderstood. All lenses of the same focal length will form an image of the same size, will include the same angle, on the same plate, provided they are capable of covering the plate, but a lens built especially for wide-angle work will have a larger field - a larger diameter of field in comparison with its focal length than a rapid (narrow angle) lens of the same focus - and will thus be capable of taking in a larger amount of view on a larger plate.
Defining Power And Definition. The terms "defining power" and "definition" are often used indiscriminately to convey the same meaning. There is, however, a difference - the difference between cause and effect. Definition is the effect, the result of the defining power of the lens. We have spoken of the image as made up of points, image points formed by rays of light reaching the lens from points on the object. If all the rays reaching the lens from one object point could be converged to one point, the image of the point would be a point. In reality, however, it is not a point but a tiny disc. The greater the defining power of the lens the more nearly to a point the rays are converged, the smaller is the disc (the more nearly it becomes a point), and the finer, or sharper, is the definition. "Sharpness," therefore, as we can readily see, is merely a matter of degree, and the question is, when can the photographic image be considered "sharp?" A disc of not more than 1-100 inch diameter appears as a point to the unaided eye at a distance of 10 or 12 inches, hence an image made up of such discs will appear sharp when viewed at such distance.