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Light Filters — Jo?ies 139
Placing 7o equal to unity we obtain
7^=1. 0-(0.0425X. 0404)
= 1.0-0. 083=. 917.
It is e\ddent therefore that the maximum intensity of any wavelength that can be transmitted through a filter having two glass air surfaces is only 91.7 per cent of the incident intensity. This 8 per cent (approximate) loss resulting from the use of a single layer of glass or gelatine, since the refractive index of gelatine is practically equal to that of glass, is not as a rule serious, but if an attempt is made to obtain some desired result by use of two or more layers, the loss of intensity due to this reflection at the glass air or gelatine air surface may become serious. In computing the loss due to surface reflection in the case of two or more superposed layers of gelatine or glass, the rather laborious step by step method illustrated above may be avoided by use of the equation,
T^=TiP (8)
in which Ti is the transmission of a single surface, p denotes the number of surfaces involved, and Tp is the transmission for p surfaces. In terms of the notation used in this paper.
For convenience in computing this equation may be expressed in logarithmic form,
log rp = ^(iog/i-i(>g/o).
In this treatment of the surface reflection losses no mention has been made of the multiple inter-facial reflections. The equation covering the case of multiple reflections takes the form of an infinite series. The magnitude of the successive terms of this series decreases so rapidly, even the second term being negligibly small, that the above form is entirely satisfactory for practical purposes.
Absorption of Radiation. The absorption which occurs within a non-turbid transmitting material follows a logarithmic law in all cases, including gases, hquids, and solids. Thus if a given layer of material absorbs a certain fraction of the radiation the next layer of the same thickness will absorb the same fraction of that transmitted by the first. If each Isijei of unit thickness transmits a fraction T (or absorbs 1 — T) then a layer of thickness x will transmit a fraction