14 



OPTICAL INSTRUMENTS. 



is called Ramsden's Micrometical Eye- 

 piece, has one great disadvantage, viz. 

 that it requires the eye to be placed ex- 

 ceedingly near to the eye-lens E. 



(23.) Being now in possession of 

 a combination that will dimmish the 

 aberration produced by the eye-piece of 

 a telescope, our limit of magnifying 

 power and light will arise from the 

 errors occasioned by the object-glass ; 

 and this, we have seen, may be dimi- 

 nished by having the curves of the two 

 surfaces as 1 to 6, with the most con- 

 vex side outermost; for this lens has 

 been shown to have less aberration than 

 any other*. Secondly, by using two 

 lenses of twice the focus in contact, to 

 produce the required refraction, and 

 thus diminish the error four times. 

 But, although this error may, by the 

 means here pointed out, be rendered 

 very small and almost imperceptible, yet 

 it is magnified in the same proportion 

 as the objects ; and when high powers 

 are used, the indistinctness will become 

 sensible. 



Sir Isaac Newton conceived that the 

 surfaces of the lens might be formed of 

 some mathematical curve which would 

 entirely obviate this error; and, by inves- 

 tigation he found that, if the surface were 

 described bythe revolution of a parabola, 

 and the radiant or object be at an infinite 

 distance, the rays would be collected to 

 a point, and be free from all aberration. 

 He afterwards formed tools to grind and 

 polish lenses of this figure, but when 

 made, although the error by figure was 

 perfectly corrected, it was discovered that 

 the white heterogeneous pencils of light 

 (before that time considered as homoge- 

 neous) in their passage through the lens, 

 were divided into their several consti- 

 tuents of red, orange, green, blue, and 

 violet, in the same manner as by a prism, 

 and hence lenses of this figure became 

 useless. 



* Dr. Brewster, in his Edition of Ferguson's Lec- 

 tures (vol. ii. p. 299), states, that in order to render 

 the common refracting telescope as perfect as possible 

 without making it achromatic, the exterior surface 

 of the object-glass should be ground to a radius equal 

 to 5-9thsof its focal length; and the radius of the 

 interior surface, or that next the eye, should be 5 

 times its focal length. In eye-glasses, the radius of 

 the surface next the object should be 9 times its focal 

 distance, and that of the surface next the eye 3-5ths 

 of the same distance. By this means, the aberration 

 arising from the spherical figure of the lenses will be 

 nothing for objects placed in the direction of their 

 axis, and the least possible for objects removed from 

 the axis. According to Huygens, the spherical aber- 

 ration was the least possible, when the radii of the 

 surfaces are as 6 to 1. But though this be true for 

 objects placed in the axes of the lenses, yet a conside- 

 rable aberration remains when the objects are placed 

 on one side of the axis. 



(24.) To illustrate the chromatic disper- 

 sion produced by a lens, let a A, Jig. 20, 

 be a white compounded pencil of light 

 proceeding from any luminous body, 

 and falling on the lens B ; parallel to its 

 axis, at the point a, this pencil of light 

 will not be refracted colourless, but the 

 red rays will cross the axis at r, and 



Fig. 20. 



the violet, which will be attracted by the 

 lens more than the other colour, crosses 

 the axis at v ; and along the interme- 

 diate space from r to v, will be formed 

 a coloured spectrum of orange, yellow, 

 green, and blue ; the proportional quan- 

 tity of these colours, and the total length, 

 will vary according to the substance 

 of which the lens is formed.* Sir Isaac 

 Newton, by most accurate observations, 

 found that in common glass, when the 

 sine of the angle of the incident rays 

 A a was 50, the sines of refraction of 

 the red and violet rays were 77 and 78, 

 the mean refraction of the pencil being 

 77. Now, if we call the sine of in- 

 cidence , the sine of refraction for red 

 rays r, and of the violet v, it is found 

 that the diameter of the circle of disper- 

 sion d s, through which all the colours 

 pass, will be as (v r) is to (v-\-r 2t ? ) 

 or as 1 to 55, so that the diameter is 

 5 ith part of the aperture of the lens, 

 which is equal to half the diameter of 

 the circle of dispersion at the focus of 

 central rays r. The circle of dispersion 

 that will comprehend any particular 

 colour, or set of colours, may be easily 

 calculated. Thus, all the orange and 

 yellow will pass through a circle, whose 

 diameter is 5 ff th of the aperture of the 

 lens. When it is considered that an 

 object-glass 5J inches in diameter has a 



* Sir Isaac Newton imagined, that the different 

 colours divided the spectrum formed by all sub- 

 stances in the proportions of a musical canon. This 

 is found to be a mistake : for when the spectrum is 

 formed by a prism of crown glass, and another of 

 precisely the same length is formed by the side of 

 it with a prism of flint glass, the confines between 

 the green and blue will be found precisely in the 

 middle of the first spectrum ; but in the second, it 

 will be considerably nearer to the red extremity : 

 indeed, there are hardly two substances that dis- 

 perse the colours in the same proportions. Oil of 

 cassia exerts the strongest action on green light, 

 and sulphuric acid the least. 



