HiSTOKY OF LIGHT REFRACTlOiN 



tive equation being: 



P J V(U + E) ds = (5) 



where U is the potential energy, 



E is the kinetic energy 



ds represents the distances involved. 

 It remained for the genius of Sir William 

 Hamilton to discover the analogy between 

 equations (5) and (-5) and to bring it forth 

 by postulating: 



y/{U + E) = 



n 



(6) 



The fundamental importance of Mauper- 

 tuis' discovery is perhaps clearly stated in 

 the following citation: "Thus, the refractive 

 index n expresses the force function or field 

 existing in matter, which results in slowing 

 down the velocity of light and determines the 

 trajectory of rays or streams of information, 

 to use modern terminology. In this sense, n 

 is a measure of interaction between matter 

 and light, and its determination contributes 

 to a knowledge of the structure of matter. 

 The abstract concept of a field of forces re- 

 mains only a convenient but arbitrary form 

 of language to explain the properties of space 

 and to predict the future behavior of the ma- 

 terial particles, the local sources of the physi- 

 cists, or points of particular chemical inter- 

 est contained in space. Thus, field of forces, 

 space properties, and the chemical proper- 

 ties of the elements are theoretical views of 

 the mind that become real, like shadow of a 

 tree, only when some interaction takes place. 

 One sees that the concept of generalized in- 

 teraction is contained in that of field, as was 

 perceived by Paul Langevin when he wrote 

 in 1903 : Tt is always matter which contains 

 the charges whose field divergence becomes 

 different from Zero.' In the absence of mat- 

 ter, indeed, 



V{U + E) = 1, 



and it is the nature of the sources that deter- 

 mines the properties of the field: if there is 

 no matter, there are no charges, no sources, 

 no force, and no field in space." (1) 



Following this discovery, the great amount 

 of experimental work stimulated b}^ the 

 theories of T. Young, A. Fresnel, and C. 

 Maxwell, all based upon the fundamental 

 concept of "field of force," revealed that, in 

 fact, the refractive dispersion of transparent 

 substances is fully governed by their ability 

 to absorb radiant energy. It is possible to 

 develop newer, more satisfactorj^ theories of 

 electromagnetism without utilizing the ab- 

 stract concepts of field of force and of action 

 at distance (24) but the antiquated field re- 

 mains a convenient means of expression. 



Today, it is admitted that the proposition 

 represented by equation (5) is valid if n 

 varies little and continuously. The "rays" 

 considered are no more than trajectories of 

 electromagnetic energy, and de Broglie re- 

 marks (25) that, in this case the treatment is 

 compatible with hath Newton's strangely 

 modern corpuscular theory and Fresnel's 

 undulatory theory. But, if n varies suddenly, 

 diffraction takes place and the concept of 

 "ray" vanishes. However, that concept of 

 refraction in the sense of Hamilton's equa- 

 tion remains valid. It is apparent from the 

 foregoing, that the determination of refrac- 

 tive indices may be accomplished essentially 

 in two ways: (a) by application of Kepler- 

 Descartes formula, involving angular meas- 

 urements, (b) by application of de Fermat's 

 principle, involving velocities, or phase, 

 measurements. The first method involves all 

 the prismatic refractometers and derived pro- 

 cedures. The second method concerns all the 

 interferometric, differential methods. From 

 this point on it is a matter of textbook record 

 that the instrumental development based 

 upon one method or the other fluctuated Avith 

 the fortunes and temporary relative impor- 

 tance of the underlying theories of light. 



REFERENCES 



1. JoNNARD, R., "Optics, a Greco-Latin Mira- 



cle," Sigma-Delta-Epsilon Lect., N. Y. 

 Academy of Sciences, Jan. 20, 1958. 



2. Teubnee, S. H., "Euclidis Optica," Heidel- 



berg, 1895. 



497 



