Method of Reducing Prismatic Spectra. 209 



whore the interference-band at X m is the mth from that at 

 X ; \ m being towards the violet, and X towards the red end 

 of the spectrum. 



The wave-length X r corresponding to any other interference 

 band (the rth from that at X ) is now immediately given by 



K=^~ (2) 



n + r 



It is therefore possible, by means of a series of interference- 

 bands produced in the spectrum in the above manner, to 

 calculate the wave-length corresponding to any part of the 

 spectrum, having given any two lines of known wave-lengths 

 sufficiently remote from each other. 



Of course it is impossible to obtain a solid film of any 

 substance whose dispersion is sufficiently small to render the 

 above reasoning even approximately correct. Recourse must 

 then be had to an air-film between two transparent plates. 

 Since the film can now no longer be placed immediately against 

 the collimator slit, some indefiniteness of the interference- 

 bands will result ; but if the plate next to the slit is not more 

 than 3 millim. in thickness no trouble will arise from this 

 cause, at any rate with a spectrometer whose collimator 

 tube is more than a foot in length. 



A very considerable improvement in the interference-bands 

 thus produced may be effected by partially silvering the two 

 surfaces enclosing the air-film. In the first place the con- 

 trast between the bright and dark bands is considerably 

 enhanced ; indeed, if both surfaces be silvered so as to reflect 

 about 75 per cent, of the incident light, the dark spectrum 

 bands become almost black. The thicker the silver is the 

 greater will be the contrast, the only limit being prescribed 

 by the diminution of the total light transmitted. 



Another important advantage gained by silvering the sur- 

 faces is the much sharper definition of the resulting bands. 

 Messieurs C. Fabry and A. Perot * have pointed out that 

 when monochromatic light is transmitted through a film 

 enclosed between two plane and approximately parallel 

 silvered surfaces, the resulting interference-bands present the 

 appearance of sharp well-defined bright lines separated by 

 broad black intervals. The explanation of this interesting 

 phenomenon is quite simple. Let the real part of gPix—W) 

 be the equation of the incident wave, whilst a and b are the 

 respective coefficients of reflexion and transmission at the 

 silver surface. Since Wiener has shown that the phase 

 change for light reflected normally at a silver surface in air 

 * Ann. Chim. Fhys. xii. pp. 459-501 (1897) 



