1 1 20 APPENDICES AND TABLES 



formulae (ii) are approximations, sufficiently accurate for general practical 

 purposes, but in cases of importance the following, longer but more 

 accurate, formulas should be used : 



. 



Plano-convex Lens. Let /=the principal focal point and y = the 

 semi-aperture ; then if parallel rays are incident on A, the plane side of 

 the lens, r = oo, and by (ii) B E = 0. The principal point is therefore at 

 the vertex B, and the focal length 



B/=^; E/=B/ 

 p-1 



The spherical aberration 



Q 



Thus when /* = , 

 SB 



8f= -4-5- ......... (v) 



If the parallel rays are incident on the convex side A, s = oo , 



h 



(vi). E/= ' ..... (vii) 



B E = -- (ii), and the focal length 



fl-l f* 



The spherical l aberration 



When /i = 1-516 (plate glass) 



/= -Mlj! ........ (viii) 



When p = l-62 (flint glass) 



8/= --8042^ ........ (viii) 



To find the radius of a plano-convex lens, the ref. index and focus 

 E/ being given : 



r=/0*-l) . I ........ (vii) 



To find the radius of a plano-convex lens, the ref. index, the thickness, 

 and the focus B/ being given : 



A plano-concave lens follows a plano-convex; / will be negative, 

 which shows that the focus is virtual. Concaves being thin, t is usually 

 neglected. 



Equi-convex and equi-concave generally: 



Equi-convex more accurately : 



1 Heath's Geometrical Ojptics, 1887. 



