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# General Properties of Optical Systems Aberrations 40

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GENERAL PROPERTIES OF OPTICAL SYSTEMS : ABERRATIONS 40. Lenses. Lenses are masses of glass, bounded, by successive moulding, grinding and polishing operations, by two spherical' surfaces, or a spherical and a plane surface. According as the beam of light emerging from a lens held up to the sun has a diminishing or increasing cross section, the lens is said to be convergent or diver gent; convergent (or positive) lenses are thicker at the centre than at the edge (Fig. 15, I to III) ; on the other hand, the edges of divergent (or negative) lenses are thicker than the centre (Fig. 15, IV to VI).

The optical (or principal) axis of a lens is the straight line joining the centres of the two spherical surfaces, or, in the case of lenses having one surface plane, the perpendicular on to that surface from the centre of curvature of the other. In every combination of lenses the optical axes must coincide ; this is known as a centred system.

41. Images Formed by Convergent Lenses. The elementary teaching of optics assumes an ideal simplicity in the instruments studied which is quite artificial (lenses of zero or negligible thickness ; rays at small inclination to the axis passing through the lenses close to the axis, etc.). These mathematical fictions can only with difficulty be applied to the complex system of the photographic lens, often working at a very large aperture over a very extended field ; it is all the more necessary to call attention to this point, as the application of the rules thus simplified may lead, by mathematical deductions which are strictly logical but ill-founded, to grossly erroneous conclusions.

When a convergent lens is placed at a suitable distance from a luminous object (or more generally any well-lighted object, stray light being excluded) it forms an inverted image which can be received sharply on a screen placed at a determined distance from the lens, this screen being, for example, a piece of white paper viewed by reflected light, or ground glass viewed by transmitted light.

42. A simple lens (reading-glass of large diameter or condenser lens), when used to pro ject the image of a window on white paper pinned to the opposite wall but placed not exactly opposite to the window, provides us an excellent lesson in optics. The image is rather poor, being spoilt by a number of defects or aberrations (the only optical instrument that can give perfect images is the plane mirror). The images of the bars will show rainbow colours (chromatic aberration), and even if this aberra tion is removed by viewing through suitable coloured filters, the image is not sharp (spherical aberration due to the spherical form of the lens surfaces). The image can be improved by cover ing the lens with a piece of paper pierced with a circular hole smaller than the lens (diaphragm or stop), but is then not so bright. Further, it is seen that the images of the bars are more or less curved (distortion), the curvature varying with the position of the diaphragm. The lens requires to be moved towards or away from the paper in order to bring the centre and edges of the image successively into focus (curvature of the field). Finally, the image of the vertical bars is not sharp at the same time as that of the horizontal bars, especially at the edge of the image (astigmatism).

43. Real Images—Virtual Images. An optical image (such as we have considered in the pre vious paragraph), capable of being received on a matt screen, is called a real image.

When a convergent lens is placed at too short a distance from an object, it is impossible to form a real image of the object at any position of the screen, but on looking through the lens an upright, magnified image of the object is seen. Such an image, visible only through the lens by an observer looking in the direction of the object, is called a virtual image. All the observational instruments (telescopes, micro scopes, etc,), adjusted for an observer with normal sight, give virtual images.

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