of the Eye-pieces of Telescopes. 37 



Ex. 1. A pencil of rays diverging from a point of an object, 

 in a plane perpendicular to the axis of a lens, passes through the 

 center of the lens : to find the distances of the planes perpendicular 

 to the axis passing through the lines of convergence. 



Here ^ is infinite, or e is infinite, and, therefore, in Fwe must neglect 

 all other quantities in comparison with e. This reduces its expression toy': 



therefore U='^±^f, Y= i^^V- 



Therefore .= S-^±i/;^, r=Z-^-^^±^f^- 

 The convergence of rays in the paper-plane, therefore, takes place in a 



nF 

 spherical surface, whose radius is ^ , and that of rays in a perpendicular 



nF 



plane m a spherical surface, whose radius is . It is remarkable that 



ra-f- 1 



these radii depend only on the focal length, and not on the curvatures of 



the surfaces of the lens, or the situation of the object. 



Ex. 2. For the camera obscura, suppose a single lens to be 

 used, with a diaphragm at a distance from the lens to limit the 

 pencil of rays : to find the situation of the diaphragm, and the 

 radii of the surfaces most favourable to the formation of a distinct 

 image. 



and the expression for V becomes 



Here e and v are the unknown quantities : since -^ =0, .-. g= 





(-i) 



