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Light Filters — Jones 137
through the front or rear surface of both as scattered or diffused Hght. Such a material is said to be turbid or diffusing. Opal glass and the developed photographic image, which consists of particles of metalhc silver embedded in a matrix of gelatine, are typical examples of diffusing materials. Diffusing materials are not in general suitable for photographic light filters and hence this paper will deal only with materials of the optically homogeneous non-diffusing type.
This case is illustrated schematically in Fig. 1 where the shaded area G represents a cross section through a transmitting material of thickness, x, and refractive index, n, bounded by the plane parallel surfaces CC and BB', Let Jo =the intensity of the incident radiation
Ic = the intensity of radiation reflected at the first surface, CC
la = the intensity of the absorbed radiation
7i =the intensity of radiation incident on the second surface, BB'
lb =the intensity of radiation reflected at the second surface, BB'
Ix =the intensity of the transmitted radiation. The transmission, T, of the filter may be expressed in terms of 7o and /i by the expression
Ji T = ~ (1)
The opacity, 0, is given by the relation,
0=l/r (2)
The optical density, D, is defined by the relation,
1 /o
D = logio 0 = logio — = logio — (3)
T I\
Surface Reflection. The intensity of the radiation reflected at the boundary surface between two media differing in refractive index may be computed by means of the Fresnel law of reflection, Tc Isin^Tz — r) Itan^Ti — r)
Rc = — = ^ -\——^ (4)
/o 2sin2(^+0 2tan2(i-r)
in which i is the angle at which the radiation is incident upon the surface, and r denotes the angle of refraction. This general form may be simpHfied in case the radiation is incident normal to the surface,
i?c = = (-— ), (5)