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Light Filters — Jones 151
Now suppose that a filter is to be used and let the transmission function of this filter be represented by curve B (Fig. 8), expressed by,
r'=/(x) (18)
the ordinate of which at any wave-length, X, is T\. By multiplying ordinates of curve A by those of curve B at corresponding wavelengths the spectral distribution of the energy reaching the photographic plate when the filter is used can be obtained. Curve C at the top of Fig. 8 was obtained in this manner. The ordinate of this curve at any wave-length, X, is
T \=JxA\T\T \.
The total photographic effect produced on the sensitive material is directly proportional to the area enclosed under curve C, this being represented by the shaded area in the figure. This area, Q, is represented analytically by the expression
AxTxJxT\Dx.
0
By using the planimeter the magnitude of this area can be determined. In this case Q was found to be 0.23 X a
Now the filter factor is given by the ratio of P, the area enclosed by curve A, to Q, the area enclosed by curve C. Expressed formally this is
P F= —
Q
f
AxTxJxd>
I.
AxTxJxT\d,
Inserting in this the values of P and Q which we have obtained by use of the planimeter it is found that
0.76a
F = = 3.3.
0.23a
The treatment of this method of computing the filter factor involving a consideration of the spectral distribution of energy in the illuminant, spectral sensitivity of the material, and spectral transmission of the filter, illustrates forcibly the dependence of the filter factor upon existing conditions. It is obvious from an exami