TELESCOPE. 



TELESCOPE. 





which the image of an object U formed at the focun of a lens or of a 

 renectin.- mirror With repect to a leiu, if it be of the kind called 

 nm*er [ LEX*], the ray* in the pencil* of light which proceed from every 

 put of an ol.jrct, as A r a,.*?. 1, in passing through the lens, supposing 



Flf. 1. 

 A 



the latter to hare a proper degree of curvature, are nude to con- 

 verge by the refracting power of the glass at points, as a, T, and 6, and 

 the assemblage of such points constitutes on image of the object : if a 

 screen were placed at P perpendicularly to the axis r r, the object would 

 be represented on it, in an inverted position. 



If the lens were of a concave form, the rays in the several pencils, 

 after passing through it, would be made to diverge from one another, 

 and consequently no image could be formed : yet if the directions of 

 the rays, after refraction, were produced backwards, they would unite 

 between the lens and the object, in points corresponding to those 

 which constitute the image formed by the convex lens. 



If the rays in the pencils of light proceeding from different points, 

 A, v, *,f3- 2 > in *" object are reflected from the surface of a concave 



Tig. 5. 



mirror, supposing the latter to have a certain degree of curvature, those 

 rays will unite in as many points, a, F, and b, and form an image of the 

 object. If a screen were placed at r the object would be represented 

 on it, in an inverted position. The rays in each pencil reflected from 

 the surface of a rmrex mirror are made to diverge from each other ; 

 and in that case no image is formed. 



Now, if the object A B be BO remote that, in each pencil, the rays 

 incident upon a lens may lie considered as parallel to one another, the 

 point T is called the principal fucut ; and in the article LENS, there will 

 be found a collection of formula; for the reciprocals of the focal lengths 

 of lenses of all the different kinds; it being understood that the 

 diameter of the lens is small, which is generally the case with telescopes, 

 and that the light is homogeneous. But, since all light is not of one 

 kind, and a lens acts like a prism in causing in each pencil the rays of 

 the differently coloured light to diverge from one another, it follows 

 that each of the coloured lights will form its own image at its proper 

 focus ; and the image formed by light of one kind being seen by the 

 eye along with the images formed by light of the other kinds, the 

 representation of an object when formed by a single lens appears 

 to be indistinct and surrounded by a coloured fringe. [ACUROUATIC ; 

 LIGHT ; DISPERSION.] It may be observed that the principal focus of 

 any lens, with respect to each colour, may be obtained from the 

 formula* in LF.XS, by substituting in them the value of p (the index of 

 refraction) for the given kind of light. 



Thus, in an optical instrument, in n<Mit!on to the distortion of the 

 image arising from the sphericity of the lens, there is an indistinctness 

 amend by the dispersion of the different colour-making rays ; an<1 , in a 

 good telescope, it is requisite that both of these imperfections should 

 as far as possible be removed. The rlirumatic atierration, as the dis- 

 persion of the colour is called, constitutes by far the greater evil of 

 the two, for Newton has shown that it exceeds the f< . iner nearly in 

 the ratio of 6449 to 1 ; but fortunately it is that whicli, to an extent 

 sufficient for practical purposes, admits of being easily corrected. 



Since different kinds of glass have different degrees of dispersive 

 power, it is evident that the chromatic aberration may be diminished, 

 if not wholly removed, by causing the light to pass through two lenses 

 of different kinds of glass, and of such forms that they may refract the 

 rays in each pencil in opposite directions. The object-glass of a tele- 

 Mope when so funned is said so be ncJurnmutir, and the m;inn. i in 

 which the effect U produced may be understood from the following 

 description. Let rq be the direction of a pencil of compound light 

 incident on the first surface of the convex lens A B, fig. 3, in a direction 

 parallel to the common axis, x T, of the two lenses. By the refractive 

 power of this lens (erotn glam) the red rays in the pencil woulil, if no 

 object were interposed, proceed in the direction 0.6, meeting x T in r, 

 and the violet ray in the pencil would proceed in the direction Q c, 

 meeting the axis in r. But the refractive power of the concave lens 

 c D (f>mt glass) acts, from its form, in a direction contrary to that of 

 the convex lens, causing the rays either to diverge from the axis x r, 



or to mi'i't it in points beyond r anil r, towards v : suppose the cur- 

 vature of this lens to be such tliat the red rays in the pencil p q . 

 after refraction in both lenses, meet the axis in F (the ray Q6r taking 



Flj. 5. 



B U 



the direction b F) ; then the dispersive power of this kind of glass 

 exceeding that of the other kind, the violet rays in the refracted ]x ncil 

 will tend farther away from the axis than the red rays do, and thus 

 will tend towards the latter; the ray Qcr, for example, taking tin- 

 direction c f. It is conceivable, therefore, that the curvatures of the 

 surfaces of the lenses may be such that, in each incident pencil, the 

 red and violet rays (the extreme rays of the spectrum) shall, after 

 refraction, unite at the place of the image ; and thus the fringe due to 

 these two colours may be destroyed. 



If the two kinds of glass dispersed the different colour-making r.iys 

 in the same proportions, their contrary refractions would cause all the 

 colours to be united on the image formed at F : no two kinds of glass 

 have, however, been as yet discovered which possess this property ; 

 and therefore the red and violet images only are united : fortunately, 

 in uniting the extreme rays of the spectrum, the others are brought so 

 near together, that for ordinary purposes the image is as free from 

 colour as can be desired. 



From the description just given it will be evident that the place F, 

 of an image in which the dispersion of the red and violet i 

 corrected, may be determined on obtaining, from the common theorems 

 of optics, algebraic expressions for the focal lengths of the compound 

 lens for each of those kinds of light, ami making the expressions equal 

 to one another. Thus, supposing R and s to be the radii of the curve 

 surfaces of a double convex lens of crown glass, and n the index of 

 refraction for light of one kind (red, for example) ; supposing again 

 that the rays in the pencils of incident light are parallel to one another 

 and pass through the lens very near the axis; then, by a fundamental 

 theorem in optics we have, P being the distance from the focus to the 

 lens, which is moreover without thickness, 



R.8 1 



~ R + S J 1 ' 



but since, in the present case, the lens may be supposed to be isosceles 



R 



(R = S), we have r= 2( _|>- 



In like manner the focal length r', of a double concave lens of flint 

 glass, R' being the radius of each surface, and /' the index of refraction 



R' 



for red rays, is equal to ztu'l)' **" ray8 ^'"S ' nci(lent near tlie 

 sic. 

 Hence, by a fundamental theorem in optics, 



and this last term is the focal length of the compound leu for red 



2(f-l) S(M' 1) 

 rays. Its reciprocal is equal to - -, , which, in the 



algebraic sense, is the sum of the reciprocals of the focal lengths of 

 the separate lenses. 



On writing n + Sp, and M' + V. in place of n and /i' in the last 

 expression, we have for the reciprocal of the focal length of the com- 

 pound lens for violet rays, 



R R' 



In an achromatic telescope the focal lengths of the compound l<-n 

 for red and violet rays are to be equal to one another; and it i 



$t* &n' 

 evident that this condition will be fulfilled when 0. From 



Ji 11 



this equation we have R : R' : : Sft : t/t'; then.divMing the antecedents 

 by ft 1 and the consequents by /'!, we have [DiSPKKSlON] the 

 ratio of the focal lengths of the two lenses equal to that of the dis- 

 persive powers of the two kinds of glass ; and hence, the focal length 

 of the compound lens being assumed at pleasure, those of the separate 

 lenses, consequently the radii of their surfaces, may be obtained. 



In order to diminish the spherical aberration, the object-glasses of 

 achromatic telescopes frequently consist of three lenses, of which the 

 first anil third are of the kind called double convex, and ore formed of 

 crown glass, while the second is double concave, and made of flint 

 gloss. In this case, since the index of refraction is the same for the 

 third lens as for the first, if the radius of each surface of the third lens 



