166 ELEMENTS OF LABORATORY WORK 



the incident wave-front, and that they are both in the same 

 plane. 



To the refracted portion of the wave the same arguments 

 and the same construction may be applied, with the exception 

 of the modification required by the difference in the speed of 

 light waves in the two media. The partial circle, which is 

 drawn from the point a in the new medium, must have a 

 radius a n which shall bear to the distance b c the same ratio 

 as the speed of light in the new medium bears to the speed 

 in the old medium. The same ratio must be observed in the 

 other cases, and a tangent drawn to the several partial circles 

 in the new medium is seen to be deflected on account of the 



Fig. 57. 



change of speed, and may be proved, as before, by applying 

 the principle of interference, to represent the refracted wave- 

 front. The incident and refracted waves are in the same plane, 

 and if at and <// stand for the angles each makes respectively 

 with the normal to the surface, then, by geometry, 



sin ({) be v 

 = or . 

 sin <j)' an v 



Or, the sines of these angles are in the same ratio as the 

 speeds of light in the two media, a ratio which is constant for 

 the same media. Hence we may ascertain relative speeds by 

 measuring refractive indices. 



