Transmission efficiency of the refractor
 

The refractor has imperfect transmission efficiency because of light losses which occur by reflection at each lens surface and by absorption in the material from which the lenses are made. When a light beam crosses a dielectric surface such as glass, a fraction of the energy is not transmitted but is reflected by the interface. At normal incidence, the fraction, R, of light which is reflected is given by
(1)
For a typical glass with n = 1·5, this amounts to about 0·04, i.e. 96% of the light is transmitted. Such a small loss hardly seems significant but when the losses from each lens surface in a multiplet lens system are summed, the total reflection loss may be quite high. For an air-spaced crown-flint doublet, reflection losses occur at each of the four lens surfaces. If the effects of multiple reflections are neglected, the transmission, T , can be written as
(2)
where nc and n f are the refractive indices of crown and flint glass respectively, since transmission equals one minus reflection. By using typical values of nc = 1·5 and n f = 1·6, equation (2) predicts that the transmission of the doublet is equal to 83%. Both nc and n f exhibit dispersion and, hence, the transmission efficiency, as determined by reflection losses, will be slightly wavelengthdependent.
Most modern lenses are finished by vacuum-depositing an anti-reflection coating on the lens surfaces to cut down on reflection losses. This process, known as the blooming of lenses, is likely to be applied to small lenses, perhaps those used in an eyepiece system but it is unlikely that a telescope of a medium-to-large aperture would be bloomed.
When energy is transmitted by transparent materials, some of it is lost by processes of scattering and absorption. The fraction which is lost depends on the actual material and the wavelength; it is also proportional to the thickness of the material through which the light is transmitted. For most ordinary glasses, absorption is not uniform across the visible spectrum. The transmission falls noticeably towards shorter wavelengths, the change in absorption becoming apparent around 500 nm or 5000 A˚ . Transmission curves for two types of glass which might be used in a doublet are depicted in figure 1. A typical large objective may be constructed by the combination of two lenses, each a few centimetres thick. With modern materials, the resulting absorption losses may be lower than 10% over the central part of the visible spectrum. However, in the ultraviolet, the absorption is so severe as to prevent observations being made in the U band.

Figure 1. The percentage transmission per 5 mm as a function of wavelength for two types of glass which
would be suitable for use in a doublet lens.

Figure 2. Simple ray diagram illustrating the ability of a spherical concave mirror to act as an image former.
(All rays are paraxial.)
 

For old established refractors, the combination of reflection and absorption losses gives values for the overall transmission for typical objectives between 50 and 70% in the central part of the visible spectrum.

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