63 



OPTICS, PRACTICAL. 



OPTOMETER. 



80 



term) shall vanish, we shall still hare one relation between the four 

 radii remaining disposable, whereby some further advantage may be 

 secured, provided it be not incompatible with those already assumed, 

 which will be known by its leading, when the condition of it is 

 expressed analytically, to an equation having only impossible roots. 

 Clairaut introduced the condition that the adjacent surfaces should 

 have the same radii, one surface being convex and the other concave, 

 so that the lenses would be everywhere in contact, and might be 

 cemented together. Instead of this, Sir J. Herschel proposes to 

 introduce the condition that the lens shall be aplanatic for pencils, 

 not only of parallel, but also of slightly divergent rays. In the 

 treatise on light above quoted (arts. 468-473), he has pointed out 

 certain advantages of this method, and has computed with different 

 dispersive ratios a table of the radii of the lenses for the compound 

 object-glass of a telescope constructed according to this system as 

 nearly aplanatic as possible, the compound focal length being lO'OOO; 

 and, by the proportions indicated, the radii for object-glasses of any 

 other compound focal length may be found. (On the subject of 

 aplanatic lenses for microscopes, see MICROSCOPE.) 



It may be well here to make a few remarks about the eye, regarded 

 merely as an optical instrument, its general structure and functions 

 being very fully'described under the article EYE, in the NAT. HIST. Div. 

 In this point of view its general office resembles that of a telescope in 

 having to form images of distant, or moderately distant objects at its 

 focus, which in order that the vision may be distinct must coincide 

 with the retina. It ditfers, however, from a telescope, in having the 

 whole space between the place of the first refraction and that of the 

 focus filled with dense matter, in not having the refraction at the several 

 surfaces centrical, and in having a much larger aperture, in comparison 

 with the focal length, than could be tolerated in the best telescope. 



On account of the magnitude of this aperture, the effect of spherical 

 aberration might be seriously inconvenient if the media of which the 

 eyB is composed were severally homogeneous and bounded by spherical 

 surfaces. The defect* of spherical aberration, it should.be remembered, 

 increase very rapidly with the aperture of a telescope, more rapidly 

 than those of chromatic aberration. It is at the surface of the cornea 

 that the main refraction takes place, and the protuberant form of this 

 part of the eye seems calculated to dimmish the aberration ; for we 

 have seen that a prolate spheroid of suitable excentricity refracts 

 accurately to a point a pencil of rays incident parallel to its axis. 

 The increasing density of the crystalline lens in passing from its 

 exterior to its centre has a similar tendency, since an ordinary glass 

 lens fails to refract a pencil of parallel rays accurately to a point in 

 consequence of the over refraction of the marginal rays compared with 

 those incident towards the middle. 



N" compensation for the chromatic aberration of direct pencils seems 

 to exist, or to be required. If a pure spectrum be thrown on a page of 

 small print, and the page be viewed by a person of ordinary sight at 

 the ordinary distance of reading, the print will be seen very distinctly 

 about the bright part of the spectrum, but somewhat indistinctly from 

 long-sightedness in the red, and very indistinctly from short-sighted- 

 ness in the violet Again, if the sun or a candle be viewed through 

 several pieces of cobalt blue glass superposed, a combination which 

 transmits only the extreme red, and the blue and violet of the spectrum, 

 the red image and the blue image, though superposed, will not be seen 

 in focus together. But in ordinary vision, where all the colours of the 

 spectrum are viewed together, the confusion arising from the imperfect 

 focusing of the fainter extremities of the spectrum is insensible. 



If the eye were perfectly invariable in form, the images of objects 

 at different distances could not all be formed on the retina, and 

 therefore, such objects could not all be seen distinctly. The eye, 

 however, possesses a power of adaptation, answering to the focusing of 

 a telescope, which accompanies involuntarily the voluntary act of 

 making the axes of the two eyes converge towards a nearer or more 

 distant object by looking at the object. 



If the cornea be too protuberant, the rays will be brought to a focus 

 before reaching the retina (unless they come from an object close at 

 hand), and the vision will be indistinct. A person thus affected is 

 said to be ilmrt-tiyhtfii. If the cornea be too flat, the rays will reach 

 the retina before they come to a focus (unless they come from a very 

 distant object, and perhaps not even then), and the vision will again be 

 indistinct, such a person being said to be lonf/-tiylited. These defects, 

 as is well known, may be corrected by the use of spectacles, re- 

 spectively concave and convex, and of suitable power. But there is 

 another defect, consisting in the length of sight being different in 

 different planes, which is far from uncommon, which cannot be 

 corrected by ordinary lenses, though it may by a properly chosen lens 

 having one or both surfaces cylindrical. [LEM8.] 



OPTICS, PRACTICAL, is that part of science which applies the 

 physical properties of LIGHT and the mathematical laws of OPTICS to 

 the construction of useful optical instruments. By the former we 

 determine the constants necessary to render the formulae of the latter 

 convertible into numbers. The refractive and dispersive indices 

 peculiar to transparent media are constants of this nature, and the 

 instruments adapted to the easy vision of near or distant objects, to 

 great or small objects, and to other optical purposes, are, according to 

 the plan of this work, described under their proper heads. [CAMERA 

 LUCIDA; HELIOSTAT; MICROSCOPE; TELESCOPE; &c.] 



ARTS AMD 8CI. DIV. VOL. VI. 



The refractive indices of transparent and semi-transparent media 

 have been a subject of research to many experimenters, and were con- 

 siderably advanced by Newton. (Newton's 'Optics.') The additional 

 properties of light discovered since his time have enabled philosophers 

 to calculate to a far greater degree of accuracy the indices both of re- 

 fraction and dispersion than was then practicable. 



The theory of achromatism, or the method of correcting the aberra- 

 tions of the rays of light, has been pursued by Euler, D'Alembert, 

 Herschel (Sir J.), and many others; but the earliest successful con- 

 struction was made by Mr. Hall, in 1733. The same was effected in 

 1757 by Dollond, whose labours, together with that of his son, gave a 

 great impulse towards the complete accomplishment of an object of 

 which Newton seems almost to have despaired. In the same career of 

 late years we must distinguish Fraunhofer, of Benediktbeuern, in 

 Bavaria, who obtained at au early age from the French Academy the 

 prize for the actual construction of achromatic glasses. Not only were 

 the necessary manual operations conducted by himself with patience 

 and the minutest attention to all the practical details of the quality of 

 his glasses and the accuracy of grinding and polishing, but he had also 

 the merit and advantage of observing the dark lines- which cross the 

 prismatic spectrum, and which are of the greatest utility in determining 

 the indices above alluded to. From the nature of the composition of 

 the glasses, some of his finest telescopes have of late become consider- 

 ably tarnished, particularly those in exposed situations. This could 

 not have been easily foreseen, and many of his telescopes remain still 

 in good condition. 



The first account of Fraunhofer 's remarkable optical discoveries is 

 given in a paper which he published in the ' Memoirs of the Academy 

 of Bavaria' for 1814-15. By means of a theodolite furnished with a 

 telescope, he measured the distances of the principal lines; and by 

 applying a photometer to the different coloured rays, he drew a curve, 

 the ordinates of which express the illuminating powers of the several 

 rays. To these researches he soon afterwards added some beautiful 

 experiments on the diffraction of light, an account of which he 

 published at Munich, and they also appeared in an abridged form in 

 the ' Bibliotheque Universelle,' January, 1822. It is believed that his 

 close application to those and similar researches accelerated his death, 

 which followed soon after. 



The accurate determination of the refractive and dispersive indices 

 has also been pursued with great success in this country, and simul- 

 taneously by some of the following distinguished men : Dr. Thomas 

 Young, Dr. Brewster, Dr. Wollaston, Sir. J. Herschel, Prof. Faraday, 

 Prof. Powell, &c. ; and in France, by Biot, Dulong, &c. ; some of the 

 results of whose experiments, in a very compressed form, are given in 

 the two following tables : 



IUFBACTIVE INDICES. 



OPTO'METER (from iirrojtai, to see, and pfrpov, a measure) is an in- 

 strument for ascertaining with precision the refractive powers of lenses, 

 and the distances at which minute objects may be distinctly seen. 

 The idea originated with Scheiuer ; but such an instrument was con- 

 structed by Dr. Porterfield, and was improved by Dr. Thomas Young. 

 It consisted of a slip of ivory, unpolished, or of wood covered with 

 white paper, about eight inches long and half an inch broad, on which, 

 in the direction of its length, was drawn a narrow and well-defined 

 black line. At one extremity of the slip was fixed a plate of ivory, or 

 a piece of card, nearly perpendicular to its length, and this was per- 

 forated either with a single aperture or with two apertures at distances 

 from one another varying from j' th to ,^th of an inch, but not exceeding 

 the diameter of the pupil of the eye. On applying the eye to a single 

 aperture, and looking in the direction of the line, drawn on the 

 instrument, the line appears to have a certain breadth, and to be ill 

 defined, at the nearest extremity : the breadth gradually diminishes at 

 points successively more remote till it becomes a minimum, when the 

 line becomes distinct ; beyond that point the line gradually increases 

 in breadth, becoming again ill defined. On applying the eye to a 

 double aperture, the line appears to be double, the parts seeming to 

 cross one another at a very acute angle, and the intersection is at the 

 place where a single line would have had the minimum breadth : 



