USEFUL TO THE MICROSCOPIST I I 19 



APPENDIX E 



OPTICAL FORMULA 



To find C, the optical centre of a lens : Let A and B be the vertices, let 

 the radius of the curve A = r, and that of B = s, t = thickness of the lens 

 and p. the refractive index. Then 



(i) 



rs rs 



Example explaining the method of treating the signs : First, it should 

 be particularly noticed that ah 1 curves which are convex to the left hand 

 have positive radii, and those turned the other way negative radii. 



In a biconvex let r = 2, s = 3, and t = 1 ; then by (i) 



A c _ 2x1 _2_ = ?. BC _ -3x1 ^^-3 _ _3 

 ~2-(-3)~2~T3~5' 2-(-3) 2 + 3 5' 



The point C is measured, therefore, to the right hand from A, and to 

 the left from B. In a plano-concave let r = 2, s = GO , and t = 1 ; then 



9 V 1 i-f^ V 1 



A ri _ _ =0' B f 1 = ' = = 1 (\\ 



~ -2- oo~ ~ -2-00 -oo " 



c is therefore coincident with A. 

 The principal points D and E may be found thus : 



A D = - . ; B E = - . -ll- (ii) 



H r s p. r s 



1 3 



Example : In a meniscus r = 3, s = 2, t = , and u = ; concavities 



4 2 



facing the left hand. 



-3 l _? -? 



1 __'j 2 "4 24231 .. 



3 ' -3-(-2) 3 ' -8 + 2 3 ' -1 3 '4" 2 

 2 

 D is measured J inch to the right from A. 



-2. 1 - -I 



BE i i. 2 _2_ _ 2 1 1 



D -t' = q O ^TA Q ' Q , O ' Q O : " " * * ' 



o o ( ,) 6 o + Z o iJ o 



2 



E is measured 3 inch to the right from B. 

 If the meniscus is turned round so that its convexities face the left 



hand, r = 2, s = 3, t = -, u. = - ; 



4 2 



1 2 ' 4 21 I 



Similarly B E = -. Both are therefore measured to the left. The- 

 2 



