of the Eye-pieces of Telescopes. 1 1 



Ex. 1. In the common opera-glass, magnifying four times, 

 to find the distortion. 



As the eye is supposed to be in contact with the eye-glass, the axis of 

 every effective pencil must pass through the center of the eye-glass. In 

 this case, then, we must trace the ray backwards, and examine its course 

 after passing the object-glass : 



iJwdl= — , C=-3F, -^^-l, e=g-^=-^: 6-5=0: 



whence Q = -r I - (n->r\ •«+ -^ ") - - (n-\-2 .v' ■\-An-^A •-/« 



4 (w - 1 )' 



25 -,A 2,71-^ ■) 



+ 3« + 2.-./-)^— ^} 



This may be put under the form 



3(n-h2) ; 3(«+l) „\- f 3m^ 6w'-28w-t-l ) 



n r"'"2(« + 2)^J U{n-\f i2ra.nT2 V ' 



or, supposing n=l,5 (which is sufficiently exact), 



„ a- r ,- 15 „x= 1811 „„) 



Hence, we find that 



1st. Q cannot be made = o. 



15 

 2d. Q is smallest when v= /: which gives r= —14 .F, 



(the negative sign showing that the surface is concave) 



14 _, _ 1811 a' 

 s = — F, Q= . -f^ . 



29 ' 504 F" 



The object-glass, therefore, is slightly meniscus ; the exterior side 

 being convex. 



3d. If the lens be plano-convex, the plane side towards the 

 eye-glass, 



„ . _ 1820 a' 



v=-f, and Q=_^^.-. 



B 2 



