Photometry

The first experiments to be performed in optics will be on the comparison of the intensities of two sources of light. We shall describe two simple methods for this, Bunsen's and Rumford's, both founded on the law that the intensity ot the illumination from a given point varies directly as the cosine of the-angle of incidence upon the illuminated surface and inversely as the square of the distance of the surface from the luminous point. So that if I, I' be the illuminating powers of two sources distant r, r' respectively from a given surface, on which the light from each falls at the same angle, the illumination from the two will be respectively I/r² and I'/r'², and if these are equal we have

I : I' = r2 : r'²,

so that by measuring the distances r and r' we can find the ratio of I to I'.

Now this supposes that it is possible to make the illumination from each source of light the same by varying the distances of the two sources from the screen. As a matte* of fact, this is not necessarily the case; in performing the experiment we compare the two illuminations by the effect produced on the eye, and that effect depends partly on the quantity of energy in the beam of light reaching the eye, partly on the nature of the rays of which that beam is composed. To define the intensity of a beam, we require to know, not merely the quantity of light in it, but also how that light is distributed among the differently coloured rays of which the beam is composed. Any given source emits rays, probably of an infinite number of different colours. The effect produced on the eye depends on the proportion in which these different colours are mixed. If they are mixed in different proportions in the two beams we are considering, it will be impossible for the effect of each of the two, in illuminating a given surface, ever to appear the same to the eye.

This constitutes the great difficulty of all simple photometric measurements. Two different sources of light, a gas flame and a candle for example, emit differently coloured rays in different proportions; the gas light contains more blue than the candle for the same total quantity of light, and so of the two spaces on which the illumination is, to be the same, the one will appear bluish, the other reddish.

Strictly, then, two different sources of light can only be compared by the use of a spectro-photometer, an instrument which forms the light from each source into a spectrum and then enables the observer to compare the intensity, of the two for the different parts of the spectrum. One such instrument will be described in a subsequent section (§67).