USEFUL TO THE MICHOSCOPIST 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 tjiat of B = s, t thickness of the lens 

 and p. the refractive index. Then 



~r-s' ~r^s 



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

 be particularly noticed that all 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) 



AC- 2xl . J = 2 - BC- ~ 8xl =-^= - 3 

 2-(-3) 2 + 3 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 = oo , and t = 1 ; then 



Ar , -2x1 n< -pp 00 X 1 00 -. /;v 



A L/ = = U I -D U = = = 1 . ( 1 1 



-2- oo -2-00 -oo 



c is therefore coincident with A. 

 The principal points D and E may be found thus : 



-; BE =.- 

 r s i r s 



1 o 



Example : In a meniscus r = 3,s = - 2, t = -, and p. = - ; concavities 



facing the left hand. 



_ 3 1 3 _3 



AD I _ J_ . ? _L = 2 -_J = 2 3 = ! (ii) 

 3 _3-(-2) 3 ' -3 + 2 3 ~ 3*4 2 



2 



D is measured inch to the right from A. 



-2.! - 1 



2 2 l l 



_ . 



- 5' _3_(_ 2 ) = 3 ' 

 2 



E is measured ^ inch to the right from B. 



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

 hand, r = 2, s = 3, * = i, /*-?; 



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



