UNDULATORY FORCES. LIGHT. 



[INDEX OF REFRACTION. 



not proceed in the straight lino e d, but is refracted or 



bent backward towards t; so that when the ray arrives 



Fig. i*. g. H 



.- " 



Fig. 15. 



f 



at a certain position in the water, it will bo observed at 

 e. The student must carefully bear in mind the direction 

 of the ray in our illustration, as entering the water. 



We will now examine the result of a ray passing from 

 any object under tho surface of the water; and, for tins 

 purpose, refer to Fig. 14, in which we find c as the point 

 from which the ray proceeds. Instead of progressing 

 from c to d in a straight line, we find that the ray is bent 

 or refracted, during its progress, from c towards e; ab 

 still remaining as a line perpendicular to the horizontal 

 surface / g. 



In Fig. 13, the angle ex a is the angle of incidence ; 

 and 6 x e the angle of refraction. In Fig. 14 we have 

 the ray of light passing from c towards d, but refracted 

 towards e." Hence b x c is the angle of incidence, and 

 ex a the angle of refraction. Now if the student will 

 carefully compare the results we here obtain, witli those 

 exhibited in the experiment with the coin and a basm of 

 water, he will at once perceive how it is that the ray 

 passing from the coin is refracted or bent back, i\s we 

 have already mentioned. The case of the fish and the 

 stick in the water are similarly explained; but in these 

 cases we deal with the ray as passing from an object 

 through a dense into a rarer medium. 



We next proceed to examine the ratio which exists 

 between tho angle of incidence and the angle of refrac- 

 tion and for this purpose we shall have to call into our 

 aid some of the laws of the mathe- 

 matical science called Trigonometry. 

 In tho annexed diagram we have a 

 circle, in which we have drawn seve- 

 ral lines. (See Fig. 15). 



The lines a c and c 6 are termed 

 radii ; and stretch, like the spokes of 

 a wheel, from the centre of the circle 

 to its circumference. The line 6 d 

 is called the sine of the angle bed; 

 and it is to this line that we have to 

 call attention in reference to the index of refraction. 



In the annexed diagram we have a circle, in which we 

 have drawn two angles. (See Fig. 16). 



In this, a e b represents the 

 angle of incidence of a ray of 

 light entering a dense medium; 

 and dee the angle of refraction. 

 Now the straight line, / g, is the 

 sine of the angle of incidence, 

 and the line h i the sine of the 

 angle of refraction; presuming 

 that the line k I represents the 

 surface of any refracting medium, 

 such as water, <tc. The index of 

 refraction is found by taking the 

 ratio which exists between the two lines or sines / g 

 and h i ; and the ratio varies for different substances, 

 M we shall see by tho following table, which gives the 

 index of refraction for several bodies. We shall give a 

 more extended series in an appendix. 



Table of Indiect of Infraction. 

 Refracting Medium. In* f Refraction. 



Vacuum 1.000000 



The atmosphere .... 1.000294 

 Ice ... 1.308500 



Water' . . 1.336000 



Fig. 16. 



Alcohol 1.370000 



1.374000 

 Florence oil .... 1.485000 



Camphor 1.600000 



-Plato glass 1.614000 



Crown , 1.626000 



1.533000 



Brazil pebble .... 1.532000 



Rock crystal .... 1.547000 



.... 1.668000 



Amber 1.547000 



Flint class 1.578000 



1.601000 



Sulphur 2.148000 



Phosphorus .... 2.2GOOOO 



Diamond 2.439000 



2.470000 



In looking over the above table of the index of refrac- 

 tion for various bodies, it will be noticed that they differ 

 very much with respect to their bending a ray of light 

 passing through them from its original straight course ; 

 and we shall observe that inflammable bodies possess this 

 power to the greatest extent. Sir Isaac Newton noticed 

 this fact, and he guessed that the diamond was composed 

 of some inflammable substance, on account of its pos- 

 sessing so high a refractive power an opinion which 

 has been verified by chemists, who have shown that that 

 valuable gem is simply a pure form of carbon or char- 

 coal. 



Having thus pointed out the nature of refraction, wo 

 proceed to explain the principles on which lenses are 

 constructed. Of these there are several kinds, tho 

 nature of which will be at once observed, as they are re- 

 presented in Fig. 17. 



Fig. 17. 



In the above diagram, the various lenses illustrated 

 have the following names : 



No. 1 is a plano-convex lens. 

 ,, 2 double convex lens. 

 ,. 3 ,, meniscus lens. 

 4 ,, plano-concave lens. 

 ,, 5 ,, double concave lens. 

 , 6 ,, concavo-convex lens. 



In the plano-convex lens, we observe that one side is 

 a plane surface, whilst the other is convex, and forming 

 part of a sphere. In the double convex lens, both sur- 

 faces are curved. The meniscus lens has a similar 

 appearance to a watch-glass, and has its opposite surfaces 

 concave and convex. In the plano-concave, we have one 

 plane, and one inwardly curved surface. In' the double 

 concave lens, both surfaces are concave ; anil in the con- 

 cavo-convex glass we have two curved surfaces, in some 

 respects like to tho meniscus glass, with tho exception, 

 however, that, in the concavo-convex, the two curves are 

 about equi-distant in every part. 



We now proceed to trace the course of the rays of 

 light passing through tho lenses of the different forms 

 above described, commencing with the plano-convex lens, 

 as, perhaps, the simplest for our purpose. 



Fig. 18. 



Let a a a a bo a number of parallel raj's of light 

 passing through the lens I I Now, it is evident 

 according to what we have previously stated, that aU 

 these rays would continue to pass in a straight line and 



