From this it is seen that reducing the aperture of the stop reduces the inequality in the bright ness of the field, but without entirely correcting given below and plotted graphically (Fig. 36) are percentages of that at the Angle . o° no° 2o° 3o° 50° 70° Illumination . Coo 94•r 78.0 56.2 34.4 Ir. I*4 The latitude is fortunately so large that a variation of about 2o per cent (which allows of an angle of 18° in the extreme pencils, or a field of 36°) is negligible, and even a variation of 40 per cent (field of 56°) is not very harmful, but for wider angles the effects of this variation become The construction of the lens almost always produces a still more rapid falling-off in ilium it, since the causes previously mentioned still operate.
A beam of obliquity equal to CC is completely stopped, and this denotes the limit of the field illuminated by the lens. These phenomena can easily be verified by moving the eye in the plane of a sharp image formed by a lens. It is then seen that the aperture of the stop DD is more and more covered by the lens rims LL and L'L', as the eye moves away from the optical axis (Fig. 38).
55. Field Illuminated ; Field Covered. We have just seen that the image plane receives no light at an angle greater than a certain value. Rotation of the secondary axis corresponding to this angle round the optical axis generates a cone of which the vertex angle (twice this limiting inclination to the axis) is the angle of the field illuminated. This cone cuts the image plane in a circle.
The image, which is sharp at the centre of the circle, becomes as a rule useless at the edge as much from want of sharpness as from insufficient illumination. If we agree to a certain tolerance in regard to definition (e.g. suppose we agree to accept for the image of a point of light a disc 1/250 in. in diameter), then at a certain aperture amounts to saying that all plate sizes of which the diagonal is less than this diameter will be sharply covered in the specified circumstances.
56. Loss of Light in Passing through a Lens. A beam of light passing through transparent matter undergoes loss, partly by absorption and partly by reflection at the entrance and emerg ence surfaces.
Loss by absorption within the glass of a modern lens is generally very small, often negligible, for visible rays. The mean values of transmission (not reckoning loss by reflection, to be examined later) are indicated below for of the diaphragm the images of distant objects will be useful within a circle, concentric with the circle of illumination, which is the circle of good definition under the given conditions. The
vertex angle of the cone formed by the secondary rays passing through this circle is the angle of field covered sharply. If the plane of the focussed image moves away from the lens (as when the object approaches it) the angle of field sharply covered remains the same, but the circle of good definition, being the intersection of the cone with a plane farther from the vertex, increases.
The employment of a small stop to improve the definition of the oblique images and to equalize the illumination over the field often has the effect of increasing the field of view as well, but this must not be taken as a general rule. Lens catalogues indicate (or should) the angle of field covered sharply for each lens at different apertures, or the diameters of the circles covered, for an object at infinity. Any rectangular shape that can be inscribed in that circle will then receive a sharp image. This different total thickness of glass, expressed in centimetres— Thickness in ern. . s 2 3 4 5 6 Transmission % . 953 93 86-4 This loss is much greater for ultra-violet radiation, which is, however, useless and indeed often harmful in current photographic practice. The loss of light by absorption may be consider able in old lenses, certain glasses of which have a pronounced yellow colouration.
Loss by reflection at the surfaces of the lens is generally more considerable than loss by absorption. In objectives containing one or more cemented lenses the loss is negligible at the cemented surfaces (about i per cent) we need therefore to consider only losses at glass-air surfaces. The mean values of transmission (not reckoning loss by absorption, examined above) are given below for one, two, three, or four lenses in air, supposing that the polish is perfect.
Number of glass-air surfaces . . 2 4 6 8 Transmission . . • - 72-1 64.6 To obtain the total transmission approxi mately, reckoning both causes of loss, it would be sufficient to multiply one factor by the other, e.g. a lens containing six glass-air surfaces in which the total of the thicknesses of the com ponents is 3 cm. transmits probably 72-1 X o-93 = 67 per cent.