GEOMETRICAL OPTI< 



1609. Find the focal length of a lens equivalent to a sys- 

 t' three convex lenses on a common axis, of focal lengt 



inches, 4 in., and 9 in. resj> i-laced at intervals >}' \ 



and 13 in., for a pencil proceeding from a point 18 in. in front of 

 the first lens. 



1610. Two thin lenses of focal lengths f lt f a are on a com- 

 mon axis and separated ly an int the axis of an eccentric 

 pencil before incidence cuts the axis of the lenses at a distance d 

 from the first lens: prove that 



F being the focal length of the equivalent single lens. 



1611. The focal length F of a single lens, equivalent to a 

 system of three lenses of focal lengths /,,/,,/, separated ly 

 vols a, b, for an eccentrical pencil parallel to the a\ 

 i by the equation 



1 1 1 1 o/l 1\ 6/1 1 



1612. Prove that tin* magnifying power of a combination of 

 three convex lenses of focal lengths f^f^f^ on a common 

 at intervals a, b, will be Independent of the 'position of the 



