The surfaces of bodies may be divided broadly into two classes, polished and diffusing, according as they reflect specularly the light they receive, after the manner of a mirror, or scatter it in all directions. A surface which scatters the light which it reflects or emits in such a way that it appears equally bright in all directions is called a "perfect diffuser." No such surface exists in perfection, but good white blotting-paper, or ground opal glass provide a fair approximation. It is sometimes convenient to use as a unit the brightness of an ideal perfect diffuser emitting or reflecting one lumen per unit area. It can readily be shown that such a surface has a brightness of i/r candles per unit area. Thus the following relationships are derived: Absorption, Reflection and Transmission.—It has been said already that bodies which are not self-luminous are visible by reason of the light which their surfaces reflect to the eye. It will be clear that, since a surface which has an illumination of one foot-candle receives one lumen per square foot, its brightness would be one foot-lambert if it were a perfect diffuser and if it reflected all the light it received. Actually, all surfaces absorb some fraction (a) of the light which reaches them and reflect or transmit the remainder. a is termed the absorption factor, while the fractions reflected and transmitted are termed respec tively the reflection factor (p) and the transmission factor (7-). For opaque bodies it is clear that ad-p=i, while for all surfaces a+pd-r= I. In general the values of these three quantities depend on (a) the direction of incidence of the light on the sur face, and (b) its colour. Only in the case of white or grey surfaces is the colour of the light immaterial. The brightness of a surface due to reflected light is clearly equal to Ep/ir candles per square foot or Ep foot-lamberts, E being the illumination in foot-candles and p the reflection factor for the particular conditions of illumi nation and the direction of view considered.
Every photometric measurement depends, ultimately, upon a measurement of the illumination produced at a surface. In the case of candle-power determination, the source to be measured and a standard of known candle-power respectively illuminate two white diffusing surfaces in a photometer head which is, in essence, a device for enabling the eye to compare the brightness of these surfaces as accurately as possible. The chief conditions for ac curacy are (a) that the surfaces shall be presented to the eye side by side with the finest possible dividing line, and (b) that the illumination of one or other of the surfaces may be varied according to a known law, so that the two may be adjusted to equal brightness. This is necessary because the eye cannot measure accurately, but can only judge of a condition of equality.
The Lummer-Brodhun Photometer Head.—The form of photometer head generally used to-day for accurate work is the Lummer-Brodhun contrast-head, the construction of which is shown in fig. 4(A). S is a matt white screen, the two sides of which are respectively illuminated by the two sources to be compared. Light from each side of S is reflected by the mirrors (or total reflection prisms) and M2 to the compound glass cube P. An enlarged view of P is shown in fig. 4(B), from which it will be seen that the cube really consists of two right-angled prisms. One of
these, is plain, while the other, P2 has its principal face etched or sand-blasted with the pattern shown shaded in fig. 4(C). The two prisms are pressed together so that the unetched parts of the surface of P2 make optical contact with the surface of The light from therefore, is transmitted through these portions just as if there were no discontinuity. The light from M2 is also trans mitted through these portions of the face of but over the re mainder, the portion shown shaded in fig. 4(C), it is totally re flected and emerges side by side with the light transmitted from It will now be seen that if the eyepiece E is focussed on the interface of P, the appearance of the field is that illustrated in fig. 4(C), the portion shown shaded being occupied by an out-of-focus image of the right-hand side of S, while the portion shown clear is filled by the left-hand side of S. Assuming complete symmetry of the instrument, it follows that when both sides of S are equally illuminated, the field of view will appear uniformly bright, and the lines of demarcation of the various parts will almost vanish if P has been skilfully constructed.
It has been found, however, that this is not the criterion of equality which the eye can appreciate with a maximum of pre cision, and the accuracy of its judgment can be materially im proved if the criterion is chanied from equality of brightness to equality of contrast. This is easily arranged by placing two thin glass plates G1 and G2 (see fig. 4[B] ) so that they are respectively in the paths of the light beams occupying the patches and R2 of the field of view (fig. 4[B]). Owing to reflection losses at the surfaces of these plates, their interposition causes the brightness of to be about 9% less than that of the background to R2, while R2 is the same amount darker than the background to It will be seen at once that, with this arrangement, if the two sides of S differ in brightness by the contrast between patch and background, instead of being 9% in both halves of the field, is 8% in one half and o% in the other, a difference which is much easier to detect than a simple 1% difference of brightness.
The Photometer Bench.—The simplest method of varying the illumination of one of the comparison surfaces in a photometer head is to move one of the sources towards or away from the head. The law of variation of illumination is then the law of the inverse square. The operation may be carried out most conveniently on some type of photometer bench. This may consist of two parallel steel bars, supported at a suitable distance apart by a rigid iron framework. Upon the bars run three carriages which respectively bear the light sources and the photometer head. These carriages run on spool-shaped wheels so that they move easily on the bars. They are provided with means for raising or lowering the sources, and for enabling them to be turned about a vertical axis. Each carriage also bears a framework on which is engraved a line situated in the vertical plane which is at right angles to the axis of the carriage pillar. This framework moves over a graduated scale attached to the bench framework. By this means the dis tances between the centres of any two carriages may readily be found.