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, formulae should be used : 



A T^ ^* ~R T7 1 ^ f"*\ 



= M (r- S )-^-l)' %(r- 8 )-*0*-l) 



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

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

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

 the vertex B, and the focal length 



= _i; E/=B/ (iv) 



The spherical aberration 



o 



Thus when p. = , 



ft 



2 



.._ 



If the parallel r&ys are incident on the convex side A, s = oo , 



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

 P 



B/= _?!--* ...... (vi). E/= * ..... (vii) 



ft-1 M /^-l 



The spherical l aberration 



, , K(fi-2) +2 y- . .... 



8/= "270^1? '/ ...... (vm) 



"When n = 1'516 (plate glass) 



S/= -1-1^ ........ (viii) 



When p. = 1'62 (flint glass) 



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



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

 E/ being given : 



l) .......... (vii) 



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

 and the focus B/ being given : 



P- 



A plano-concave lens follows a plano-convex ; f 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 lloalli's Geometrical Optics, 1887. 



