USEFUL TO THE MICEOSCOP1ST I I 29 



An excellent combination, suitable for a bull's-eye, can be made of 

 boro-silicate glass, refractive index 1-51, i> = 64'0 



1st lens 1 crossed r = + 2-359),. - 



s= + 15-078 f aiam< 



2nd lens 1 meniscus r = + 1*280 i ,. 



8= - 3-434 J diameter ! 



Distance between lenses, -05 ; equivalent focus, 2-0 ; back focus, 1-55 1 

 total aberration, - '103 ; clear aperture, 2-0 ; angle, 62. 

 This combination is eminently suitable for photo-micrography, and for 

 those cases where a bull's-eye is necessary. 



A simpler form of bull's-eye cafti be made of two pianos, using the 

 same glass ; see fig. 9, p. 1128. 



1st lens, radius + 3*0, diameter 2'1 

 2nd +1-8 1-9 

 Distance between lenses, -05 ; equivalent focus, 2. 



To find the radii r and s of a lens which will refract light from a point 

 jp to point p' with minimum aberration. 



Let /3 be the coefficient of ^- in formulae v, viii, xi, and xv, then for 



parallel rays in each particular case the lateral aberration = ^-- /3 . . (xlv) 



1 y 3 

 Diameter of least circle of aberration = j% & ...... (xlvi) 



Distance of least circle of aberration from focus = - ^- . (xlvii) 

 ' When the rays are not parallel 

 (xlv) = a>j2/2/ 3 (xlvi) = -up'y 3 (xlvii) = -|a>.pV 



It is interesting to note that^- =2(/u 1)^ ....... (xlviii) 



Therefore, when ^ = . , y ~ = i. 

 * J 



To find m, the magnifying power of simple lenses or magnifying 

 glasses. Let d be the least distance of distinct vision apart from the lens, 

 and / be the principal or solar focus of the lens. Then, when the eye is 

 held close to the lens, 



m = 1 + A- . . . ..... (xlix) 



When the eye is held at the back principal focus of the lens, subtract 

 one from this quantity. For real images projected upon a screen, the 

 distance of the screen being d, subtract two. 



It may be of interest to note that formula (xix) on this page may be used 

 to determine the focus of spectacles required to bring the abnormal focus 



1 In this formula the convention used with regard to the signs is that of manu- 

 facturing opticians, and not that employed in the rest of the appendix. 



