OPTICS. 



till the other foot falls at E' into a circle 

 E' Q' A' passing through A', and having 

 C' for its centre, taking care that the 

 point E' is such that when one foot is 

 placed there the other foot can touch 

 C Q' in no other point but F'. But as 

 the ray is now passing out of glass into 

 air, A'D' is the sine of the angle of inci- 

 dence, and E' F' the sine of the angle of 

 refraction ; hence the line C' E' drawn 

 through E' will be the refracted ray. The 

 refraction of the prism has, therefore, 

 bent the ray A C, which would have 

 gone on to m, into the line C' E', which 

 forms with A m an angle E'rcra, which 

 is the deviation or change of direction 

 of the ray ; so that if the ray A C pro- 

 ceeded from the sun, or from a candle, 

 it would, by an eye placed at E', be seen 

 at a in the direction E' n a, and the 

 angle of deviation will be A n a equal to 

 E'wra. 



In the case shown in fig. 4, the re- 

 fracted ray C C', in passing through the 

 prism, is parallel to its base R R', and 

 when this is the case, the angle of devi- 

 ation A n a is less than in any other 

 position of C C', and, consequently, of 

 A C, as may be easily proved by con- 

 structing the figure for any other position 

 of these rays. If, therefore, we place 

 the eye behind the prism at E', and turn 

 the prism round, we shall at once ascer- 

 tain that C C' is parallel to the base 

 R R', by the image of the candle at a 

 being stationary ; for, in every other 

 position of A C and C C', that image 

 will move towards a'. When we have 

 thus placed the prism in this position, 

 or so that the ray C C' is parallel to 

 RR', or perpendicular to 8 T, a line 

 bisecting the refracting angle of the 

 prism RS' R', then it is obvious that the 

 angle of refraction at the first surface, 

 viz. E C F, is equal to R S T, half of the 

 angle of the prism. Now, as half this 

 angle is known, and as it is easy to 

 measure at once by a Goniometer*, or 

 divided instrument of any kind, the 

 angle of incidence AGP, we have, 

 without any further trouble, the angle 

 of incidence, and the corresponding 

 angle of refraction at the surface R' S'. 

 By making the following proportion, 

 therefore as the sine of the angle of 

 refraction is to the sine of the angle of 

 incidence, so is unity to the index of 

 refractive power that is, dividing the 

 sine of the angle of incidence by the 



sine of the angle of refraction, we obtain 

 the refractive power. This is the sim- 

 plest of all methods, and the most gene- 

 rally applicable for measuring refractive 

 powers, because soft solids and fluids 

 can be placed in the refracting angles 

 of hollow prisms made by joining two 

 plates of parallel glass. 



Refraction through plane glasses. 

 LetMN, (Jig. 5.) be a plane glass, and 



Fig. 5. 



*Frora two Greek words,- 

 angles. 



ignifying measure of 



A C a ray of light refracted at C on 

 entering the glass, into the direction C c, 

 and at c on going out of the glass, into 

 the direction c a : if we determine the di- 

 rection of the refracted rays C c and c a 

 by the method shown iny?g\ 2, we shall, 

 find at once that c a is parallel to A C ; 

 for however much A B is bent out of 

 its direction at the first surface of the 

 glass, it is bent just as much in the op- 

 posite direction, at the second surface, 

 so that it is restored to its original di- 

 rection. It will appear, however, to an 

 eye at a, as if it came in the direction 

 A/ c. Every person is accustomed to 

 observe that the plane glass of windows 

 does not alter the position of objects seen 

 through it, except in particular parts 

 of the glass, which will be found, upon 

 examination, to be places where the two 

 faces are not parallel. 



Refraction through lenses. Although 

 we have hitherto spoken only of the re- 

 fraction of plane surfaces, yet most of 

 the refractions we have to consider in 

 optics take place at spherical or other 

 curved surfaces. This circumstance, 

 however, does not add any difficulty to 

 the subject, for the refraction which 

 takes place at a curved surface of any 

 kind is exactly the same as at a plane 

 surface which touches the curve surface 

 at the point on which the ray falls. If, 

 for example, the ray A C (fig. 2.) falls 

 upon the curved surface r C s at C, and 

 if R C touches r C s at the point C, then 

 the small portion of the curved surface 

 at C, which is concerned in refracting 

 the ray, may be considered as a part of 



