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138 Transactions of S.M.P.E., August 1927
in which n is the refractive index of the material and is defined by the ratio
sin i n = — (6)
sm r
In the case of hght filters as used in photography the departure from normal incidence is so little that no appreciable error results from the use of equation (5). The value of n, the refractive index, depends upon the wave-length of the radiation, hence Re also depends upon wave-length. The variation of n with wave-length in the case of glass and gelatine, the materials commonly used for fight filters, is so small as to be of fittle practical significance. Assuming that the wave-length range of interest in photographic work extends from 350 m/x (the shortest wave-length transmitted by the glass of which photographic objectives are made) to 800 m^t (the longest wavelength to which photographic materials are sensitive) the variation in n for ordinary crown glass is from 1.535 (wave-length = 350 mju) to 1.511 (wave-length = 800 mju). This variation is less than 2 per cent, and since Ic is approximately 4 per cent of 7o it is evident that the variation with wave-length of the intensity of the radiation transmitted by the surface is for all practical purposes negfigible. For dry gelatine the variation of n with wave-length is of the same order of magnitude and hence for all practical purposes the use of equation (4) will give results of sufficient precision. By substituting in (4) the numerical values applying to ordinary crown glass we
obtain,
/1.519-1\2
Ic = h{ =/oX. 0425 = 4. 25% of /o.
\1. 519+1/
Assuming now that the absorption, la, of the material is negligibly small, this being true for visible wave-lengths in the case of thin layers of colorless glass or clear sheet gelatine, 7i becomes equal to Iq — Ic Equation (4) may again be used for computing the reflection at the second surface, BB'. This takes the form
Using the numerical values for glass and solving it is found that 76= 0.0404/0
I. = h-{Ic+I,) . (7)