82 



PHOTO-MICROGRAPHY 



there is no refraction or reflection — the only instance where it undergoes no bending — 

 for it passes on into the water, uninterruptedly following the course of the line E D, 

 But when it is incident at any other position — say at m along m E there is refraction 

 at E, for the beam will be found to strike the point n. Suppose it is incident at m' 

 along m' E, then there is also refraction at E, for the ray will be found at n'. 



Snell made a celebrated investigation concerning this bending of the rays, by 

 which their path can be predicted. Were it not for his discovery, about to be 



explained, we should not have had the grand compu- 

 tations of lenses with which, in the present day, we 

 are all so familiar. 



He first drew a line from m to meet B E at o, and 

 another from n meeting E D at p. The lengths o m 

 and n p were measured and divided one by the other ; 

 a quotient was obtained. Now what he discovered 

 was the fact that wherever the angles were taken, 

 whether from m or m', the quotients, in all cases 

 using water and air, came out the same, viz., i'S2>3- 

 This was called the refractive index of water. Other 

 substances were tried, and each substance had its special refractive index. Flint 

 glass, for instance, was found to be about i "54 to i "64, according to its manufacture, 

 and so on with other substances, complete lists being found in all books upon the 

 subject. If the reader be mathematically inclined, he will at once see these lines, 

 m o, n p, really represent the sines of the angles B E m and n E p respectively, so 

 that, continuing our precept, the sines bear certain definite ratios one with the other 

 wherever the incident light striking E comes from ; that is, the ratio between o m 

 and n p, which is about 4 to 3, holds good, whether the ray starts from m or m^ It 

 is quite evident now that we can calculate where the ray will strike A D, after starting 

 from any given point in B C. For example, let m strike E to make an angle m E o, 

 say, of 45°. It is required to find the angle n E p, so that we can draw n E 

 correctly. We take out of the tables the sine of 45", and find, roughly speaking, it 

 is 07, and multiply that by 3 and divide by 4, which gives us 0*5. Resorting to our 

 book again, we find 0*5 is the sine of 30", so that 30° must be marked off from D to 

 find the line n E. Although, simply put, this is the maxim which mainly pervades 

 the optician's mind in constructing new lenses. As a matter of fact, the details 

 become exceedingly operose in real calculations, as different colours are refracted at 

 different angles, and the problem, where many lenses are concerned, becomes intensely 



