TELESCOPE. 



Table I. Theorems for finding the rtfraded Foci of Lcnfts. 



Lenl'es with unequal Radii. 



Kiys. 



Diverging 



Parallel 



Converging 



Convex. 



(/R; 



<j</c + fl^R — /• R 



= /• 



R 



flR 



= /• 



- rfrR 



— adr — a^R — r R 



/• 



Concave. 



rfR, 



— adr — atiRr— Rr 



= /• 



R 



— ar — a R 



= /• 



- </rR 



flf/r + ad'R — rR 



= /• 



Lenfes writh equal Radii. 



Diverging 



2 ad ■ 



= /• 



- dr 



2 ad + r 



■I- 



Parallel 



r.=/- 



Converging 



- dr 



— 2 ad — r 



= /• 



2 ad + r 



= /• 



Lenfes with one Radius (R) infinite. 



Piano-convex. 



Plano-concave. 



Diverging 



dr 



id- 



= /• 



- d r 

 ad + r 



= /• 



Parallel 



■■/■ 



~-f- 



Converging 



- dt 



ad - 



= /■ 



- dr 

 a d — r 



-/• 



Lenles with one Radius (R) negative, or Menifci. 



Unequal. 



Equal. 



Diverging 



drK 



adr — adR + rR 



= /■ 



d=f. 



Parallel 



,R 



- aR 



■/■ 



~^=f- 



Converging 



drR 



adR — adr + rR 



= /■ 



d^f. 



Lenfes with both Radii (r and R) negative, or double concave. 



Diverging 



Parallel 



Converging 



drR 



— adr — adR — rR 



= f, always negative. 



R 



aR 



■zz. f, always negative. 



drR 



ad r + adR — rR 



= /• 



