Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/44

 bance at the instant t is simply the envelope of the secondary waves which arise from the various surface elements of the original wave-front. The introduction of this principle enabled Huygens to succeed where Hooke and other contemporary wave-theorists had failed, in achieving the explanation of refraction and reflexion. His method was to combine his own principle with Hooke's device of following separately the fortunes of the right-hand and left-hand sides of a wave-front when it reaches the interface between two media. The actual explanation for the case of reflexion is as follows:—

Let AB represent the interface at which reflexion takes place, AHC the incident wave-front at an instant t0, GMB the position which the wave-front would occupy at a later instant t if the propagation were not interrupted by reflexion. Then by

Huygens' principle the secondary wave from A is at the instant t a sphere RNS of radius equal to AG: the disturbance from H, after meeting the interface at K, will generate a secondary wave TV of radius equal to KM, and similarly the secondary wave corresponding to any other element of the original wave-