168 Transactions of the Society. 



then 



r - 2Q*-l)/ . 



ce + 1 ' 



2Q-1 )/ 

 c e — 1 



s = 



Example. — When /x = 1 ■ 5, p = 10, and/ = 1, then c = - 0*8, 

 e = -0-7143, and ce = 0-5714. 



r =™T-i = r^ii = ' 636; 



s = = _ _ o • qqq 



0-5714 - 1 -0-4286 ~ 



Therefore r : s : : 1: - 3*666, the lens is biconvex with its flatter 

 curve towards the eye ; when p is infinite, then the ratio of the radii 

 is 1 : — 6, but when p is equal to 2 / the lens becomes equiconvex ; 

 if p is less than 2 /, the flatter curve must face the object-glass, but 

 this latter case will hardly ever occur. 



Eye-lens. — To find the radii when the focus, the refractive index, 

 and the ratio of the radii are given. Let k be the ratio of the radii, 

 then kt = s, and s = (ji — 1) (# — 1) f- 



s 

 r = - ; 



K 



Example. — Let/ = 2, //, = 1 • 5, and r : s : : 1 : — 3 ; then — 3 r— 

 s, and k = — 3. 



s = 0-5 x -4 x 2 = -4; 



r = ~ 4 = 1 • 333. 

 -3 



The lens is therefore biconvex. 



The following is the trigonometrical method of tracing a ray : — 

 h is the distance from the axis where the incident ray meets the field 

 lens, and h' where it meets the eye-lens (fig. 43). The angles cor- 

 respondiDg to the natural tangents can be found in Chambers' Mathe- 

 matical Tables, and to trace the ray no knowledge beyond that of 

 simple arithmetic is required. 



p' = -^L-- q = d-p'; c[ = JL' ; h' = ^; tan 6 = - ; 

 p-f q-f -p p 



h h' 



tan ^ = - ; tan = - ; S = e + </>; 8 = R - <f>. 

 p q 



