OPTICAL IMAGES. 



from the lens L L. In that case, the distance of the.red image R' t 

 from L' i/, will be greater than that of the red image R from L L, 

 and in like manner the distances of all the intermediate images 

 of o' o' from I/ if will be greater than those of the corresponding 

 images from L L. 



Thus the coloured images of o' o' produced by L' i/ will be 

 spread over a greater space than those of o o produced by L L. 

 The dispersion of the latter is therefore greater than the dispersion 

 of the former. 



"With the same amount of refraction, therefore, the lens L' L' 

 produces more dispersion than the lens L L. 



If we suppose the convexity of the lens L L to be increased, the 

 refraction will be increased, the image v will be produced at a 

 less distance from it, and at the same time the dispersion v R will 

 be increased. The convexity, as shown at L" L" (fig. 34), may be 

 so much increased, that the dispersion v" R" shall be equal 

 to V R'. 



Thus it appears that a diamond lens, which would have a dis- 

 persion equal to that of a glass lens, would have a much greater 

 refraction, and would produce the image of the same object much 

 closer to it. In a word, the focal length of a diamond lens having 

 the same dispersion as a glass lens, would be much shorter than 

 the focal length of the latter ; or, what is the same, with an equal 

 focal length, the diamond lens would have a less dispersion. 



64. It appears, therefore, in general, that lenses made of 

 different transparent substances will have, under like conditions, 

 different dispersions. The DISPEESIVE POWERS of any two 

 transparent media, will be measured by the dispersions which 

 lenses of the same focal length made from them would produce. 



The actual DISPERSION produced by a lens must not be con- 

 founded with the DISPERSIVE POWER of the material of which 

 the lens is formed. 



The actual dispersion produced by a lens of a given material, 

 varies with its focal length, and with the distance of the object 

 from it, so that with the same lens there may be many different 

 quantities of dispersion, and the quantity will also be different 

 with different lenses of the same material. But the dispersive 

 power depends on the material alone, and is altogether independent 

 of the form of the lens, its focal length, or the position of the 

 object relatively to it. It will be most important that this dis- 

 tinction should be understood and remembered. 



65. It might be imagined that the dispersive power would 

 necessarily increase with the refractive power of the transparent 

 body. On comparing together the optical effects of different 

 media, no such correspondence is however found to prevail ; on 



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