the Slit in Interference Experiments. 477 



small fraction of /3AAy, and referring' to the results obtained 

 above, we see that in the case of FresneFs mirrors, and in 

 the cases of the biprism and of the divided lens when the 

 thickness is neglected, /3/y^a/b, so that the condition for 

 maximum distinctness is that the width of the slit must be a 

 small fraction of a/b times the width of the bands, where 

 a and b are the distances of the interference apparatus from 

 the slit and screen of observation respectively*. 



In the case of the biprism when its thickness is neglected, 

 if a and b alone vary, their sum remaining constant, «A 

 is constant, and hence, in order that the distinctness may 

 remain unchanged, the width of the slit must be inversely as 

 b, that is the narrower the bands, the greater the admissible 

 width of the slit, 



Starting from the case of maximum distinctness and 

 gradually increasing the width of the slit, we see that the 

 interference-bands will become less and less distinct ; they 

 then vanish and reappear again in the complementary 

 position, since sin (iryk/\)/(7ryk/\) changes sign on passing 

 through the value zero, and increase in distinctness up to a 

 maximum which is about a fifth of the prime maximum of 

 distinctness, and so on. 



An interesting method of observing this phenomenon is to 

 allow white light to pass and to subsequently analyse the 

 mixture by a spectroscope with its slit placed at right angles 

 to the interference-bands. When the source of light is a 

 narrow slit, the ordinary fan-like appearance is obtained, 

 that is a spectrum traversed by slightly curved bands running 

 more or less along the spectrum and approaching one another 

 towards the violet end. As the source of light is gradually 

 made wider the bands become less distinct, the distinctness 

 decreasing most rapidly at the violet end, until a region with 

 no bands takes its rise at that end and passes along the 

 spectrum to the red end, to be followed by a second such 

 region and so on, the bands on the two sides of the bandless 

 region being complementary. 



This method also affords a means of determining the u limit 

 of visibility " for a given wave-length ; for by using a 

 micrometer slit as the proximate source of light and adjusting- 

 its width until one of the limits of the bandless region 

 coincides with a given Fraunhofer line, the quantities that 

 occur in the expression for the visibility may be determined 



* In other words, the angle subtended by the slit at the interference 

 apparatus must be a small proportion of that subtended by the width of 

 the bands at the same point, a result that might be arrived at by 

 elementary reasoning. 



FhiL Mag. 8. 5. Vol. 46. No. 262. Nov. 18 c Jb. 2 L 



