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Color Filters or Color Screens 53
making the wedge. As all dyed filters dry with a slight shift in absorption towards the red, allowance was made for this ; therefore, two other glasses were coated with slightly smaller amounts of solution and then dried rapidly with a fan. Exposure to the spectrum was then made through each and any further correction noted.
The Action of a Filter on the Image. — It may be useful to consider the action of a filter on the image. Let AB, Fig. 10, represent a plane parallel plate of glass, and 0 an object from which proceeds the light-ray OC, incident on the front surface of the glass at C. The distance of the point O from the plate being Oa, then the ray is refracted at the surface of incidence towards the normal and apparently proceeds from P. The refracted ray strikes the second surface at D, and the distance DP is equal to afji-\-t ; fx being the refractive index of the glass, and t its thickness. After refraction by the second surface B, the emergent ray appears to proceed from the point Q, and the distance QB is equal to a-\-t/fx. As the distance of the point O from the second surface is equal to a plus t, the apparent shift in the direction of the axis and towards the glass is (a-\-t) — (a-\-t/fx) the angle of incidence being assumed to be large. It will thus be seen that the shift is dependent on the thickness t of the glass plate and the refractive index, and not on the distance of the point O from the plate. The action of a filter in front of a lens is shown in Fig. 11, in which a ray proceeding from the point O is refracted by the lens, without a filter, to the point P. But if we insert a filter it will, as before, take the dotted path, and the image be formed at 0', and the ground glass must be shifted by the amount S'PP' from the lens.
If the incident ray is prolonged backwards, as shown by the dotted line, it will cut the axis at 0', and the axial shift S is equal to 00', in the object space, and is equal to t(fi — 1 )/[i, as pointed out above. If the size of the image to the object is called r, then the well known ratio is S:S' :: r2 : 1. it naturally follows that S' : S : r'-, and the shift of the ground glass as the
fl-1 1
result of the insertion of the filter in front of the lens is S*=i X •
If we assume the thickness t of the filter as being 3 mm. and the refractive index of the glass as 1.5, for we can neglect the thickness of the gelatin and its refractive index, then using the previous formulas we have (fL-l)/(ju=$ and t(/a-l) /n=l mm. The shift of the ground glass is S'=l//x2 mm. If the ratio of the object to image is large, or in other words, if the distance of the object is great in comparison, then 1 : r is small and l///.2 disappears. It is only when reproducing to a comparatively large size, that is the reduction is small, that we have to take into account the shift of the object in focusing.
If the filter is placed behind the lens, as in Fig. 12, it will be seen that the rays from the point O cut the axis at P without the filter; but by