46 



BELL. 



law established by Fresnel. In any lens system of free surfaces /' = 

 7 (1 — K)'^ where /' is the transmitted light and k is Fresnel's factor 



M 



M 



, , . The transmitted light is then, for unity incident light, 

 1 — fc)". For practical purposes k varies from a scant 4% in light 



crown glass to 6% or a little more in dense flint, averaging perhaps 

 ."»% in lenses as they are found in practice. The total light thus 

 reflected, and lost to the incident ray as such, evidently increases 

 rapidly with the number of surfaces, and runs about as follows: — 



TABLE 



Measured transmissions are often several per cent, below these figures. 



This last case includes prism glasses and ordinary terrestrial tele- 

 scopes. No account of loss from absorption as such is here included. 

 Absorption ordinarily amounts to between 1 and 2% for 1 cm. thickness 

 following the usual exponential law for greater thicknesses. It does 

 not bear any particular relation to the index of refraction until one 

 comes to very dense flints when the absorption is specific in the blue 

 and violet. More light is lost in a single reflection than in several 

 cm. of glass. For our present purpose no account is taken of loss 

 from imperfect polish, and dust, which may produce some scattering 

 and obstruction of light. 



Now the ghosts, visible as such, or spread o\-er the whole field, have 

 an aggregate intensity equal to the total light lost by reflection, and 

 they may be divided into two series, odd and even with respect to the 

 number of reflections. All the odd series are directed toward the 

 incident ray and in themselves produce no visible effect, save as they 

 may be reflected from the inner side of diaphragms. In some instances 

 they may become objectionable, since the diaphragm is likely to be 



