ON THE GENERAL LAWS OF OPTICAL INSTRUMENTS. 275 



when 0,6, becomes parallel to the axis). The point F, may be found, by 

 remembering that A l a 1 = B 1 b 1 , A 1 a t = xA 1 a l , B}) 1 = yB}> l . We find 



y-x 



Let <7 a be the point at which the emergent ray is at the same distance 

 from the axis as the incident ray, draw gfr^ perpendicular to the axis, then 

 we have 



y-x 



Similarly, if a^ l F l be a ray, which, after emergence, becomes parallel to 

 the axis ; and g^Cr, a line perpendicular to the axis, equal to the distance of 

 the parallel emergent ray, then , 



x-y 



Definitions. 



I. The point F lt the focus of incident rays when the emergent rays are 

 parallel to the axis, is called the first principal focus of the instrument. 



II. The plane G^ l at which incident rays through F l are at the same 

 distance from the axis as they are after emergence, is called the first princi- 

 pal plane of the instrument. F& is called the first focal length. 



III. The point F z , the focus of emergent rays when the incident rays 

 are parallel, is called the second principal focus. 



IV. The plane &&, at which the emergent rays are at the same distance 

 from the axis, as before incidence, is called the second principal plane, and 

 Ffr t is called the second focal length. 



When x = y, the ray is parallel to the axis, both at incidence and emerg- 

 ence, and there are no such points as F and G. The instrument is then 

 called a telescope. x(=y) is called the linear magnifying power and is denoted 



ft 



by I, and the ratio ' is denoted by n, and may be called the elongation. 



c i 



In the more general case, in which x and y are different, the principal 

 foci and principal planes afford the readiest means of finding the position of 

 images. 



352 



