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

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Light Waves and Their Uses

The resolving power, as shown in one of the preceding lectures, depends on the size of the diffraction rings which are produced about the image of a star. It was also shown that the smallest angle which a telescope could resolve was that subtended at the center of the lens by the

radius of the first dark ring, and this angle is equal to the ratio of the length of the light wave to the diameter of the objective. For example, if we consider a 4-inch glass, the length of the light wave being of an inch, this

angle would be If

the lens were a 40-inch glass, the angle would be something like YwJ-crrro, which can bo represented by the angle subtended by a dime at the distance of fifteen miles. Hence, if we had two such dimes placed side by side, the largest glass would scarcely separate them.

Fig. 90 is an actual photograph of the image of a point of light taken with an aperture smaller than that of a telescope, but otherwise under the same conditions under which a telescope is used. It is easy to see that, surrounding the point of the image, there is a more or less defined white disc, and beyond this a dark ring. Outside of this dark ring there are a bright ring and another dark ring. Theoretically, there are a great number of those rings; practically, we see only one or two under the most favorable conditions.

This figure represents the appearance of the image of one of Jupiter’s satellites as it would bo observed in one of the largest telescopes under the most favorable conditions. If it be required to measure the diameter of one of these very

Interference Methods in Astronomy

distant objects, a pair of parallel wires is placed as nearly as possible upon what is usually called the edge of the disc, as shown in Fig, 91. The position of this edge varies enormously with the observer. One observer will suppose it well within the white portion; another, on the edge of the black portion. Then, too, the images vary with atmospheric conditions. In the case of an object relatively distinct there may be an error of as much as 5 to 10 per cent. In many cases we are liable to an error ^ „

FIG. 91

which may amount to 15 per

cent., while in some measurements there are errors of 20 to 30 per cent.

Suppose the object viewed were a double star. In general, the appearance would be very much like that represented in Fig. 92, except that, as before stated, in the actual

case the appearance would be troubled by “ boiling.” It will be noted that as long as the diffraction rings are well clear of each other we need not have the slightest hesitation in saying that the object viewed is a double star.

Fig. 93 represents under exactly the same conditions two points, artificial double stars, but very much closer together. In this case the diffraction rings overlap each other. It will be seen that the central spot is elongated, and the expert