Michelson A. A. Light waves and their uses (1903)

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Light Waves and Their Uses

thickest at the center, the retardation is greatest there, gradually diminishing toward the edge. The effect is to change the form of the wave front from a plane to a spherical shell,














FIG. 19

which advances toward the focus at O, and produces at this point a maximum of light, which is the image of the point whence the waves started.

Fig. 20 illustrates the case where the convex waves diverging from a luminous point O are changed to concave waves converging to form the image at O'.

It can readily be shown that the luminous point and its image are in the same line with the center of the lens —

FIG. 20

sufficiently near for a first approximation. Accordingly, if we take separate points of an object, we can construct its image by drawing straight lines from these through the center of the lens, as shown in Fig. 21. The size of the image will be greater the greater the distance from the lens, so that


the magnification is proportional to the ratio of the distances from object and image respectively to the center of the lens; hence in the microscope an error in determining the position of the image means a much smaller error in the determination

of the position of the point source. This error could be diminished indefinitely by increasing the magnifying power, were it not for the attendant loss of light and the fact that the light waves, though very minute, are not infinitesimally small. In fact, the same diffraction effects again limit the possibility of indefinite accuracy of measurement. What, then, is the new limit?

Let p, Fig. 22, represent the center of the geometrical


image of a luminous point. This will be a point of maximum brightness, because all parts of the concave wave which converges toward/; reach this point at the same time, and therefore in the same phase. Let us consider an adjacent point q. The parts of the converging wave are no longer at equal