The operation which we call `focusing' is a very sophisticated one which we take very much for granted. But how do we actually perform it? Even a very brief thought will make it clear that what we really do is to make the image look as we think the object is meant to look. We assume, for example, that if in one position of the lens all the junctions between black and white areas are sharply defined, then it is probably `in focus'. The assumption clearly is that the junctions really are sharp. If on the other hand the object on the slide already had diffuse junctions it would be correspondingly more difficult for the projectionist to focus the slide. In the event of real difficulty we may focus on a hair, or on some specks of dust, which we assume should have `sharp edges' and hope that when they look right the whole slide will be right. There are in fact, whether we like it or not, only two ways of focusing; one is to calculate the precise position of lens, slide, screen, etc., on the basis of geometrical optics and the other is to work on the basis of some preknowledge about the nature of the object. We shall return to the implications of this statement for X-ray diffraction at a later stage.
With visible light we can usually solve the focusing problem fairly easily and images of extremely small objects may be produced in the optical microscope. One severe limitation however, is the wavelength of light and detail below this size cannot be imaged. One alternative is to use electrons whose wavelength is quite small enough, but the practical problems of lens designs for the electron microscope provide an experimental limit before the resolution of individual atoms can be achieved.
X-rays have a suitable wavelength and would provide a simple solution if they could be focused experimentally. Unfortunately this is not possible except with systems of curved mirrors which are capable of only very limited magnification. To achieve the full benefits of the small wavelength some alternative approach must be adopted.
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