G20 Transactions of the Society. 



grow as long as the edges of the slit send out light not more than 

 90°, or \ wave-length, out of phase with light from the centre of 

 the slit ; if the slit becomes still wider, the intensity of the dif- 

 fraction spectrum is diminished, and becomes zero when twice the 

 previous width is reached, i.e. when light from the edges of the 

 slit is £ wave-length out of phase with that from the centre. Up 

 to this width the combined phase is the same as that yielded by 

 a grating of indefinitely narrow slits. But when the width of the 

 slits is increased still further, the diffraction spectrum re-appears, 

 and gains an equally bright maximum at a difference of phase of 

 | wave-length between centre and edges, declining beyond that 

 point and once more disappearing when the difference of phase 

 becomes a whole wave-length. But, and this is my great point, in 

 this second cycle the sign of the resulting amplitude is reversed, 

 i.e. ths combined phase is in this case the opposite one to, or is 

 £ wave-length different from that given by indefinitely narrow 

 slits. As all trigonometrical functions have a period or cycle of 

 360°, it is evident that when the differences of phase between 

 centre and edges of a slit exceed a whole wave-length, the result- 

 ing integral phase will be the same as that for the excess over a 

 whole number of wave-lengths — i.e. for a difference of phase of, 

 say, 3£ wave-length", the resulting combined amplitude and phase . 

 would be the same as for a difference of \ wave-length. 



It will now be easy to apply this law to the successive diffrac- 

 tion-spectra of a plane grating. 



In the first spectrum, the difference between the light from 

 adjoining slits is one wave-length, and the difference of phase 

 between centre and edge of any one slit cannot exceed £ wave- 

 length, as at that point the adjoining slits would coalesce. There- 

 lore it follows that the first spectrum is always in phase with 

 the direct light ; we can also see that the brightness of the first 

 spectrum will be a maximum when the slits are equal in width to 

 the intervening dark spaces, for that corresponds to the difference 

 of phase of 90°, for which we found the maximum value. 



In the second spectrum, light from adjoining slits differs by 

 2 wave-lengths, and our angle /3 can therefore reach 360°, and 

 produce any of the values in the table. In this case we shall 

 therefore have — 



The diffraction-spectrum is in phase with the direct light when 

 the slit is narrower than the dark space, i.e. /3 < 180°. 



The diffraction-spectrum is in opposite phase to the direct light 

 when the slit is wider than the space, i.e. /3 > 180°. 



The second spectrum wall have maxima of brightness when the 

 width of the slit is respectively \ or f of the spacing of the grating ; 

 it will vanish when the slit is equal to the dark interval. 



Proceeding to the third spectrum, where light from adjoining 

 slits joins up with a difference in phase of 3 wave-lengths, /3 can 



