1893-94.] Mr G. A. Berry on Focus of Concavo-Conmx Lenses, 193 
along the axis (measured from the other surface) at which a ray 
parallel to the axis before refraction meets it after refraction, has 
the following values according as the ray impinges on the convex 
or concave surface first : — 
From fig. 1- 
F = 
Esin 
sin{ (« - r). - {r' -i')} 
where E is the radius of both surfaces, and i, i' and r, r' the angles 
of incidence and refraction at the two surfaces. The relation 
between these angles is given by 
and 
sin?^ =/>tsinr, 
sin / = (X sin i " , 
sin i' = sin r — sin {i - r) . 
From fig. 2 — 
and 
VOL. XX. 
F = 
sin i 
E sin r' 
sin{(r' -'i')- (i - r)} 
= sin r + g sin (^ - r) 
) 
12/4/94 
X 
