Author: J.B. Hoag
There is an analogy between the action of light rays in optical systems such as lenses and prisms, and the action of electron streams in electric and magnetic fields.
|Fig. 21 A. A comparison of light rays passing through glass systems (on the left) with cathode rays in electrostatic fields (on the right). (From E. & N. P.)|
Suppose a ray of light were to pass through a glass prism as in Fig. 21 A (a). It would be found that the blue rays of light are bent more than the red rays of light. Now consider the analogous case of a narrow pencil of electrons passing between two metal plates, one charged plus and the other minus, as at (a') of this figure. Since the faster electrons remain in the electrostatic field of the condenser for a shorter period of time, they are bent away from their straight line path less than are the slower electrons. The light rays are dispersed by a glass prism into their component colors, and the electron rays are dispersed into their different electron speeds. We conclude that there is a reasonable comparison between the extent to which different colors of light are bent and the extent to which different velocity electrons are bent. Now, there is a quantity in optics, called the index of refraction, which serves as a measure of the extent to which light rays are bent. We may, analogously, use the velocity of the electrons as a measure of the extent to which they will be bent. It can be said at this point, without further details, that it is possible, starting from this analogy, to carry over en masse the mathematics of optics to serve as the mathematics for the calculation of the action of both electric and magnetic fields upon rays of electrons in vacuum tubes.
Figure 21 A (b) shows the focusing action of a glass lens upon light rays, while (b') shows the analogous focusing action of two negatively charged balls upon a parallel beam of electrons. It is to be remembered that electrons are negatively charged and are repelled by the negative charges of the balls. It is necessary that this repulsion increase by the proper amount off the axis if electrons at different distances from the axis are all to come to the same focal point.
Figure 21 A (c) shows how a bi-concave lens diverges the rays of a beam of parallel light. Analogously, the two positively charged metal balls of (c') of this figure diverge the electrons in such a way that they spread out. They all appear to have come from a common source on the left of the charged balls.