188 



UNDULATORY THEORY OF LIGHT. 



In the otlier case, it will be observed that the rays I and I' undergo repeated 

 reflections between the surfaces of the plates — a 

 portion of the light escaping and being ti'ansmitted 

 at each reflection. If the plates are of perfectly 

 equal thickness and all the surfaces perfectly par- 

 allel, there will be no interference. Suppose, how- 

 ever, that one of them is slightly thicker than the 

 other. Then, if we attend first to the transmitted 

 rays, T, T', we shall see that the path of T, after 

 incidence and up to final emergence, is made up of 

 three times the thickness of the first plate, once 

 the thickness of the second, and once the distance between the plates. Put d 

 for the first thickness, 0' for the second, d for the distance between, and L for 

 the length of path. Then — 



Tracing back T' in the same way, and denoting its length of path by L', we 

 have — 



Hence 'L'—L=2{0'—0). 



And when this value is so small as to be comparable to the absolute thicknesses 

 which produce the colors of Newton's rings, similar colors may be seen here. 



If we attend to the reflected rays R and R', we shall see (employing the same 

 notation as before) that — 



V—2()+20'+28. 

 Hence L'— L=2 {O'—O), as before. 



It will be noticed that there are other rays, as r and t, which do not form tints, 

 their difiereuces of path, as compared with R, R', or with T, T', being too great. 



§. VII —POLARIZATION BY REFLECTION AND BY REFRACTION. 



We will now proceed to give a physical theory of the phenomenon called 

 polarization of light, and of its production by reflection and refraction. It has 

 already been hinted that the phenomenon itself consists in the determination of 

 the molecular movements in the succession of undulations which constitutes a 

 ray or beam of light, to one constant azimuth, or definite direction in space ; 

 those which exist in common light being distributed impartially through all 

 azimuths. In order to simplify tlie problem of the influence of reflection upon 

 molecular movement Mr. Fresnel commenced this investigation by consider- 

 ing first the case of a wave polarized already in the plane of incidence. In 

 such a wave the molecular movements arc (for reasons which will appear here- 

 after) presumed to take place in a plane whch is at right angles to the i)lane oj 

 'polarization. At the reflecting surface, they are therefore coincident with the 

 surface itself. If the ray is passing from a medium of less refracting power 

 into one of greater, we must suppose that the ether possesses either a ditterent 

 elasticity, or a different density, or both, in the two media. Mr. Fresnel assumed 

 a difference of density without a difference of elasticity. He assumed, secondly, 

 that in the common surface or stratum bounding the media, the movements 

 parallel to the surface are common to both media, so that the components of 

 velocity in the incident and reflected wave, parallel to the surface of reflection, 

 are together equal to the component of velocity in the transmitted wave parallel 

 to the same surface. Or, if unity represent the incident molecular velocity, v 



