GHOSTS AND OCULARS. 47 



as good or better a reflector than a glass surface. The coefficient of 

 reflection generally is nearer 10 than 5 % for it is a very dense and 

 perfect black indeed that falls below 5%. The ghosts of even order, 

 however, furnish light traveling with the incident ray and conse- 

 quently the even order ghosts bi'ing light directly into the field and 

 may become distinctly visible. 



In general the total of the reflected light is divided into ghosts of 

 the odd and even series in the approximate ratio k : k^. If P be the 



P 



total reflected light, then any 1st order ghost must be less than — , 



71 



2kP 

 any 2nd order less than — ; — . 



•^ n{n-l) 



More precisely the ghosts of the first order odd series have intensi- 

 ties kl, kl(l — ky, kI(l — kY and their sum is, putting t = (l—k) 



Si =^ kl {I -\- f + t' h i^'^-i) 



while the second order ghosts, even series,^have an approximate total 

 intensity P IV\ since each ray concerned has to pass at least n surfaces, 

 in average somewhat more. 



Intensities of Individual Ghosts. 



Since ghosts of the 3rd order have coefficients in k^ and pass forward 

 they may practically be neglected, and those of the 4th order likewise, 

 having, even if in focus, magnitudes at least 14-15 m. less than the 

 primary image from which they are derived. 



Of the 71 ghosts of the 1st order none can cause trouble save indi- 

 rectly, as already shown. 



7i(n — 1) 

 There are 2nd order ghosts and the maximum brightness of 



any one ghost in focus must be at least 7.5 m. below its primary. In 

 ordinary objectives and photographic doublets the 2nd order ghosts 

 are 7.5 to 8.0 mg. below the primary even when in focus. The differ- 

 ence can readily be measured by bringing the principal ghost to the 

 area of its primary by changing focus and then using a photographic 

 wedge to measure the relative intensities. The difference in bril- 

 liancy comes out at approximately 7-8 m. 



Cemented surfaces may practically be left out of account since for 



