118 A. A. Michelson — Measurement hy Light-waves. 



In the telescope the size of the image and hence the magnification depends en- 

 tirely on the focal length. The resolution is in this case the reciprocal of the 

 smallest angular distance which can be clearly distinguished. It increases with 

 the diameter of the objective and inversely with the wave-length. These for- 

 mulas may also be applied to the revolving mirror as used in galvanometers, etc., 

 except that in this case the accuracy is doubled, so that 



'A=2eB/2,. 



The foregoing statements must be understood to refer to theoretically perfect 

 lenses. If the lenses be imperfect the ratio of their performance to that of a perfect 

 lens may be expressed by a constant depending on the accuracy of the surfaces 

 and the nature of the glass. 



The first named qualifications depend on the accuracy with 

 which all parts of the lens contribute to make the elementary 

 waves reach the focus in exactly the same phase. But this is 

 not at all necessary for " accuracy." For this purpose it would 

 be as well to entirely annul the central portions of the lens (or 

 mirror) leaving only an external annular ring ; or better still 

 only two small portions at opposite ends of a diameter need be 

 used ; and this too without any sacrifice of accuracy but on the 

 contrary a very considerable gain. For it is now possible to 

 increase the size of the interference fringes up to any limit 

 without affecting the light ; and the result is exactly the same 

 as could be obtained with a perfect microscope of infinite 

 magnifying power with an infinitely bright source of light. 



These two small portions to which the lens is thus reduced 

 need not be curved, but may be either plane mirrors or prisms. 

 Thus the telescope or microscope will have oeen converted into 

 a refractometer. 



The details of the various forms which the instrument may 

 take, their classification, and their older and better known ana- 

 logues, are shown in the diagrams, Plate III. 



Description of Plate. 



In the first four groups the paths of the two pencils are equal. 



Group I. — Waves emanate at a point and converge at another. Nos. 1 and 3 

 are the types; 2, represents Fresnel's mirrors; 4, Billet's half-lenses ; and 5 r 

 Fresnel's bi-prism. In this group the diminution in intensity is the same as in 

 the microscope. 



Group II. — In this and the succeeding groups a pencil of rays divides at a 

 plane surface and reunites at another. No. 1 is the type (a simple microscope 

 objective). Nos. 2 and 3 are forms appropriate for linear measurements; 4, 5, 6 

 and 7, for differential measurements. 4 and 5 show the essential part of the re- 

 fractometer of Jamin and of Fresnel respectively. (The latter does not belong to 

 the group, but serves as a type for 6 and 7.) 



Group ILL — In this group the pencils retrace their path, and reunite' at the 

 same surface, o, where they separate. Fig. 1 is the type for 2 and 3. These 

 figures represent the original form from which the others have been derived.* 

 They may be used for absolute or differential linear measurements. 



Fig. 4 is the type for 5 and 6 which are appropriate forms for angular measure- 

 ments; in fact just as the angular motion of the mirror mm of 4 is detected by the 

 motion of the image at o, so that of the mirrors mm of 5 and 6 is detected by the 

 motion of the interference fringes at o. 



* See " Interference phenomena in a new form [of refractometer," A. A. Mich- 

 elson, this Journal, Art. xlvi, p. 395, 1882. 



