REFRACTION THROUGH LENSES. 473 



rays passing from right to left, and by/ for rays from 

 left to right. The rays A d and A g pass, after refrac- 

 tion, in directions df and A g, which do not intersect 

 but diverge and appear to proceed from the point a ; 

 a is the virtual image of A. Similarly the rays B h f 

 and B i give b as image of B, and consequently the total 

 image a b is virtual, erect, and magnified, and is situated 

 on the same side of the lens as the object. The image 

 can obviously only be seen by an eye which is so placed 

 as to receive the rays after passing through the lens ; 

 in the figure the eye would have to be situated on the 

 right side of the lens. 



The distance of an image from the lens is calculated 

 by rules which correspond to those given with reference 

 to concave mirrors (see page 448). The magnitude of 

 the image is also found similarly, but in a lens the 

 magnitudes of object and image are proportional to their 

 distances from the centre of the lens, while in a mirror 

 they are proportional to the distances from the centre 

 of curvature. 



Lenses should have a small curvature if they are to form correct 

 images ; the curvature of lenses may however be much more con- 

 siderable than that of mirrors without producing distortion. The 

 glass of which the lens is made must not only possess the correct 

 outline of a portion of a sphere, but the glass itself must be of 

 uniform quality throughout. The best lenses are very expensive : a 

 single biconvex lens of a superior kind, 6 cm in diameter, is worth 

 several pounds, while a common lens of the same size, such as those 

 used for burning-glasses, may be had for a few shillings. 



Expensive lenses are principally required for the better kind of 

 telescopes. For the following experiments in which we simply study 

 the different kinds of images produced by lenses, a large lens such 

 as a reading glass, and several smaller ones (for experiments to be 

 described hereafter) are quite sufficient. 



In these experiments the diameter of the lens is assumed to be 

 6 cm , the radius of curvature of each surface as 30 cm , the focal length 



