It has been noted that certain spectrophotometric curves, especially those of the sharp cut-off type of colored glasses, have essentially the same shape—merely displaced in wave-length for different thicknesses. If this were strictly true, it must be that the curve between log log transmittance and wave-length is a straight line, since only a straight line can be moved vertically (by change of glass thickness) and match the same curve moved horizontally (by change of wave-length). If it is assumed that the log log transmittance versus wave-length curve is a straight line the curve between transmittance and wave-length has an S shape which is not a bad fit for actual spectrophotometric curves of certain glasses. If the fit were perfect, the wave-length displacement of the curve caused by change in thickness would be proportional to the change of the logarithm of thickness, the constant in the equation can be determined by the slope of the curve. With a series of infinitely sharp cut-off curves in which there is complete transmission for all wave-lengths greater than a certain wave-length, and complete absorption for all shorter than this, the values of Y, x, y, and z (Transmission and x, y, and z I.C.I. Coordinates), may be calculated. A wave-length of cut can be found which will produce the same chromaticity, x and y coordinates as any of the sharp cut glasses but the transmission will differ, being the maximum possible for the given chromaticity. The change in chromaticity expressed as change in y coordinate can be determined relative to change in wave-length of cut-off. By combining this latter relation with the change of wave-length of cut-off caused by change of thickness of the given glass as determined from the shape of the log log curve it is possible to calculate the required change in thickness to produce any desired change in the y coordinate within the capabilities of the glass.
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