66 Mr. A. Whitwell on the Lengths of the 



The line oc making an angle 6 1 with the vertical line oo' 

 (fio-. 7) represents the axis of the first lens of which the focal 



length is f. The line oh making an angle 6 2 with the line 

 oo' represents the axis of the second lens the focal length of 

 which is/ 2 . Let a, b (fig. 7) be the points of incidence of 

 two horizontal parallel rays symmetrical with respect to the 

 line oo'. The axial semi-aperture oo' = hi; the tangential 

 semi-aperture o'a = o'b = h 2 . 



Consider first the ray incident at a. The first lens alone 

 will deflect the ray in a plane at right angles to the axis f Y . 

 The line ac (fig. 7) will represent the emergent ray, the 

 point c being at a perpendicular distance /\ from the lens. 

 The second lens alone will deflect the ray in a plane at right 

 angles to the axis f 2 . The line ad (fig. 7) will represent the 

 emergent ray, the point d being at a perpendicular distance 

 f 2 from the lens. In the line ad take a point e such that 



ae 

 ad 



Then the lines ac, ae, will represent the deviations in the 

 focal plane of the first lens due to the two lenses separately 

 and the diagonal a /of the parallelogram a cef will represent 

 the deviation due to both lenses acting together *. 



The line af also represents in end view the ray after it 

 has emerged' from both lenses, and the line of (tig. 8) will 

 represent the ray in front elevation ; of (fig. 8) being made 

 = f v The line" ff x (fig. 8) represents tHe trace of the focal 

 plane of the first lens. 



Consider secondly the ray incident at b. The first lens 

 alone will deflect the ray to a point g distant f x from the 

 lens ; the second lens alone will deflect the ray to the 

 point h distant / 2 from the lens. 



In the line b h take a point i such that y^y- Tnen as 



* See Chapter X. Handbook of Optics, by W. N. Suter. Macmillan 

 & Co., 1899. 



