COLORS OF THIN PLATES. 183 



siu5 is unity, indicating a deviation of 90^. A grating, llicrerorc, in Avliicli the 

 number of lines to the inch is equal to the number of unduLutions in the same 

 space, will produce no spectra. The same is true, a Jhrtlvri, of still liner 

 gratings 



The s])ectra formed in this way by diffraction will easily be understood to 

 form the best of all possible measures of the lengths of the undulations corres- 

 ponding to the different colors. They exhibit very distinctly the principal lines 

 of Fraunhofer; and these lines, as might be inferred as a theoretical necessity, 

 preserve invariably the same relative distances from each other. The spectra 

 formed by refraction afford measures, not of the relative lengths of the undula- 

 tions in vacuo, but of those lengths as modified by the media of which the 

 refracting bodies are composed. Apparently these modifications are not simply 

 proportional to the lengths of the undulations. Mr. (Jauchy's investigations 

 upon dispersion shovv, as we have seen, that they ought not to be. 



Light rrjlected from finely ruled surfaces exhibits colors, as well as that which 

 is transmitted through them. These effects arc produced by interference, and 

 are explained upon principles analogous to those we have been considering. 

 Some substances are naturally marked with sinuosities which produce these 

 effects. A familiar example of this kind is seen in mother of pearl. Sir David 

 Brewster found that an impression of the polished surface of this material taken 

 in wax, exhibited the same colors as the substance itself. 



The effects produced by diffraction may be endlessly varied, by emjdoying 

 (instead of gratings) reticulations, and groups of apertures, of various ffgures, 

 symmetrically disposed. Many of the phenomena arc exceedingly rich and 

 beautiful. We must content ourselves with the examples which have been 

 given, and which illustrate the general principles on which they all depend. 



^ VI. COLOKS OF THIN PLxVTES. 



We will now proceed, very briefly, to apply the tlieory of undulation to the 

 explanation of the colors seen in thin transparent plates ; or, as they arc com- 

 monly called, Newton's rings. These, when seen by reflected light, arc caused 

 by the interference of the wave which proceeds from the lower surface of the 

 plate with that which is reflected by the up])cr. Let us suppose, at first, for 

 simplicity, that the light employed is homogeneous. Where the dark rings 

 occur, there must be a dififereuce of path between the interfering waves, of one- 

 half an undulation. Now the wave which is reflected from the lower surface, 

 passes through the thin plate twice ; and that which is reflected from the upper 

 surface does not enter the })late. • The difference of path is therefore twice 

 the thickness of the plate ; and this ought apparently to be equal to half an un- 

 dulation, or to some uneven multiple of half an undulation. Let represent 

 the thickness, and n any integral number; then — 



26'-— (2«+l)Xi!.'^^ : and when n=Q, 20^^h,L or 0=^^).. 



It should seem, accordingly, that the first dark ring should appear, Avhere the 

 thickness is equal to one-quarter of the length of an undulation. As the thickness 

 increases toward cy^r--.];., or diminishes toward 0^0, the light should gradually 

 appear ; and when either of these va'ues is reached, wo should have the maxiniun of 

 brightness. The centre of the system should then be bright. It is not so, hoAv- 

 ever, but on the other liand is entirely dark. The reason of this apparent dis- 

 cordance with theory will be understood, when wc recall the circumstance, 

 thus far disregarded, that the reflection at the lower surface takes place as 

 the ray is proceeding from a rarer to a denser medium ; while that at the 

 first surface occurs as the ray is passing from a denser and to a rarer. 

 It has been already shown that, in the latter of these cases, the molecular move- 

 ments maintain their original directions ; while in the former, these movements 



