Interference-Bands. 89 



g lvin g A x cos {kat — ^z—px—fi) (10) 



A photographic plate exposed to this would yield no impres- 

 sion, since the intensity is constant. 



In order, then, that a grating may be capable of giving rise 

 to the ideal system of interference-fringes, and thus impress 

 itself upon a sensitive plate at any distance behind, the 

 vibration due to it must be of the form 



A cos (px+f) cos [hat— fi ± z) (11) 



It does not appear how any actual grating could effect this. 

 Supposing 2=0, we see that the amplitude of the vibration 

 immediately behind the grating must be a harmonic function 

 of x, while the phase is independent of x, except as regards 

 the reversals implied in the variable sign of the amplitude. 

 Gratings may act partly by opacity and partly by retardation, 

 but the two effects would usually be connected ; whereas the 

 requirement here is that at two points the transmission shall 

 be the same while the phase is reversed. 



We can thus hardly regard the interference-bands obtained 

 from a grating and Lloyd's mirror as a mere reproduction of 

 the original ruling. As will be seen in the following para- 

 graphs, much the same result may be got from a prism, in 

 place of a grating ; and if the light be sufficiently homogeneous 

 to begin with, both these appliances may be dispensed with 

 altogether. 



Prism instead of Grating. 



If we are content with a less perfect fulfilment of the 

 achromatic condition, the diffraction - spectrum may be 

 replaced by a prismatic one, so arranged that d(k/b)=Q 

 for the most luminous rays. The bands are then achromatic 

 in the same sense that the ordinary telescope is so. In this 

 case there is no objection to a merely virtual spectrum, and 

 the experiment may be very simply executed with Lloyd's 

 mirror and a prism of (say) 20° held just in front of it. 



The number of black and white bands to be observed is not 

 so great as might perhaps have been expected. The lack of 

 contrast which soon supervenes can only be due to imperfect 

 superposition of the various component systems. That the 

 fact is so is at once proved by observation according to the 

 method of Fizeau ; for the spectrum from a slit at a very 

 moderate distance out is seen to be traversed by bands. If 

 the adjustment has been properly made, a certain region in 

 the yellow-green is uninterrupted, while the closeness of the 

 bands increases towards either end of the spectrum. So far 



