490 The Curvature Method of Teaching Optics. 



confusion. Or in focal lengths we have 



Primary focal length f x —f ^ 1 - (2p + 1) ^ r 



Mean „ „ f =f -{ 1 - (f* + 1) f f > 



.r <£ 2 1 



Secondary „ ,, f 2 =f< 1— — > 



Curvature of Focal Surfaces. — In order that the oblique foci 

 should lie on a plane through the principal focus we have 



ft — F cos </> = F i 1 — ^ \ approx. 



If A^ is the excess of the actual convergence over that 

 necessary to focus on the plane, we have 



sag A./ = F2 , 



and lateral distance of focus from principal focus 



tan d> d> 

 ■i' = ~J = J approx. 



Hence curvature 2 £f 2A<^ 



= -5=- = ,,- approx. 



Applying this to the above we have : 



Curvature of primary focal surface, B^ — e F = 3F + — 



„ of surface of least confusion, R — - — — F = 2F + 



/* /* 



,, of secondary focal surface, E 2 = F = F+ -. 



A 6 At 



The corresponding radii of curvature can be at once written 

 down and are in agreement with those given by Mr. Dennis 

 Taylor and others "*. It is also obvious from the method of 

 proof that the curvature of the image surfaces is independent 

 of the position of the object plane. 



Focal Surfaces for Thin Lenses in contact. — Since the 



curvature is given by — g- , and the convergence of any 



* H. Dennis Taylor, " Design of Telescope Object Glasses," Proceedings 

 Royal Astron. Soc. 



