REFRACTION THROUGH LENSES. 471 



pass through the middle of the lens retain their original 

 direction, because the two opposite faces of the lens are 

 parallel near the centre, and the rays are therefore re- 

 fracted twice equally, but in opposite directions. The 

 lateral displacement of the ray (see fig. 259, page 457) 

 may in this case be neglected. This has a sensible 

 effect only if the light falls in a very oblique direc- 

 tion upon glass, and if the thickness of the latter is 

 considerable ; but in the determination of the optical 

 images of lenses, only those rays fall under consideration 

 which proceed from points near the axis, and which are, 

 therefore, nearly perpendicular to the middle of the lens. 

 Let A B in fig. 270 represent an object of which the 

 distance from the lens is twice the focal length, / being 



the principal focus for rays which proceed from left to 

 right ; for parallel rays passing from right to left, the 

 corresponding focus would be in c. The ray A d, 

 parallel to the axis, is refracted to the focus /, and 

 proceeds after refraction in the direction d-f a ; the ray 

 from A which falls upon the centre passes through the 

 lens in the same direction, viz., e a; both rays meet at 

 , and in the same point all other rays from A converge : 

 hence a is the image of A. Similarly the rays B gfb 

 and B e b determine the point b where the image of B is 

 produced. The image of A B is thus a b ; it is real, 

 inverted, has the same magnitude as the object, and 

 image and object are at the same distance from the lens. 



