I I 22 APPENDICES AND TABLES 



t-ltt-2 



B/- 



(xiv) 

 Similarly A/ = -2* (xiv) 



By (xii) and (xiii) 



This is larger by ^ g inch than the result obtained by (xiv). 

 The following is an example worthy of note. Suppose 



r-s<t and >(>-!)-. 

 Thus let r = 5 -. s = 5, t = 1, p =|. 



5 ^1_11\ _155 

 Then by (xiv) B/ = ^ = -2- = -310. 



2\2~3/ 12 



It will be observed that, although this meniscus is thickest in the 

 middle, it has, however, a large negative focus. 



The principal points of a sphere are at its centre. 

 The focus of a sphere, measured from the centre : 



E f = ^ r (xvi) 



J 20* -1) 



The focus of a sphere measured from its surface : 



B '-;-|^T>- ^ 



The focus of a hemisphere measured from the plane surface, the light 

 being incident on the convex surface : 



B/= ^ (vi) 



But when the light is incident on the plane surface, the lens being 

 turned round : 



B/ 



When p. = 1'5 the focus of a sphere measured from the surface = the 

 radius. 



The focus of a hemisphere measured from the plane side = 1^ the 

 radius, and when measured from the convex side the focus = 2 radii. 



In a cylindrical lens the principal points cross over. 



To find the radii r and s of a crossed lens of minimum aberration for 

 parallel rays : 



