REFRACTION 23 



favorite analogy for our light-beam and our pair of optically different 

 substances. Suppose a platoon of soldiers to be marching over bare 

 ground toward the edge of a wheat-field, which is at an angle to their 

 line of march (Fig. 8). The ranks of soldiers now represent successive 

 wave-fronts in a light-beam, and their files represent the individual light 

 rays in the beam. Obviously the soldiers cannot march as fast through 

 the dense wheat as over open ground, so that the latter may represent 

 air, and the wheat-field a piece of glass of high optical density. 



As the first soldiers in the front rank start into the wheat, they are 

 slowed up, but those at the other end of the front rank are still able to 



A 



A -0- -^ 



f 



Fig. 9 — Step-by-step explanation of the focusing of parallel rays by a convex lens. 



a, displacement of ray by tilted plane-parallel plate (compare Fig. 8). b, bending of ray 

 by prismatic plate, c, approximation of parallel rays without convergence, by pair of tilted 

 plane-parallel plates, d, convergence of parallel rays by pair of prismatic plates, e, inde- 

 pendent foci of pairs of parallel rays, through action of prisms placed base-to-base, 

 ■f, coincidence of foci when slope of prism faces is decreased toward their bases, g, single 

 focus of all parallel rays, resulting when process in f is fully carried out, yielding a 

 smoothly-curved lens. 



march rapidly since they have not yet reached the wheat (Fig. 8a). 

 Consequently the front rank is swung around as if hinged at one end, 

 and by the time the whole of the rank is in the wheat, it has taken a 

 new direction of march which is of course followed by each rank in the 

 whole platoon (Fig, 8b). Upon emerging from the wheat-field on 

 the other side (Fig. 8c), the process is reversed and the platoon's line 

 of march becomes parallel to its original one, displaced laterally a dis- 

 tance which depends upon the width of the wheat-field and the difficulty 

 of marching through it. 



