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# Wavelength Dependence

Author: J.B. Hoag

There is no simple relationship between the color or wave-length of the incident light and the photoelectric current. Furthermore, different sources of light give off different wave-lengths in different proportions, as shown in Fig. 20 E.

 Fig. 20 E. Relative energies of light radiated at different wave-lengths as compared with the response of the human eye to these colors. (From E. & N. P.)

The light from the sun is of more nearly constant intensity throughout the visible spectral region than is the light from a tungsten filament lamp, where the redder rays are much stronger than the blue rays at the other end of the spectrum.

Let us suppose, however, that there existed a source of light which gave out rays of equal intensity at each wave-length throughout the visible spectrum, from the extreme reds through the extreme violets.

Let us separate this composite light, color by color, and let each in turn fall upon the cathode of a photoelectric cell. The photoelectric current per unit intensity of light is called the yield. Let us now examine the curves of Fig. 20 F.

 Fig. 20 F. Spectral distribution curves of some photo-emissive surfaces. (From (E. & N. P.)

Only the general shape of the curves has significance; not their absolute values. One can readily see that at certain favored wave-lengths the photoelectric current (per unit of light intensity) is very much larger than at other wave-lengths. This is called spectral selectivity. It is to be noticed that the photoelectric currents are larger for a cathode surface coated with one material than with another. For light rays of about 0.000,043 cm. (a deep purple color) the potassium surface emits electrons copiously. For a surface of cesium on cesium oxide on a silver base there are two favored colors, one a very red color at about 0.000,07 cm., and the other in the extreme ultra-violet region beyond the range of the eye, at about .000,035 cm. Although retaining their general shape and peaks, the curves for a given cathode surface will be found to differ somewhat according to the method of manufacture of the cell. All of this means that certain types of phototubes are preferable for use in one part of the spectrum and others are preferable for other colors.

An important point to be noted in connection with the curves of Fig. 20 F is that they plunge into the horizontal axis at a definite point. This long wave-length is called the photoelectric threshold. Light of greater wave-length than this threshold, falling upon the cell, will fail to eject electrons from the cathode, while shorter wave-lengths will do so.

The actual photoelectric currents emitted from a given photoelectric surface by light from a given source can be determined: (1) by multiplying the corresponding ordinates of the two curves in Figs. 20 E and 20 F, and (2) measuring the total area under the resulting curve.

In order to specify the current from a photoelectric cell, it is necessary to state both the intensity and color of the incident light.

The yield from an exceedingly sensitive photoelectric cell is about 600 micro-amperes per lumen. This corresponds to 5.8 · 10-13 ampere for the smallest amount of light visible to the human eye (9.6 · 10-13 lumen when the pupil diameter is 6 millimeters). Ordinarily, photoelectric cells at best deliver from 20 to 100 micro-amperes per lumen. In sound-on-film, the light flux varies from about 0.01 to 0.04 lumen. Then the current output is a few micro-amperes. The current through a small light bulb is roughly 1,000,000 micro-amperes. In other words, photoelectric currents are quite small and require either delicate indicating instruments or vacuum tube amplifiers.

Last Update: 2010-11-21