52 E. I. Gal'perin et al. 



of the net (in our case between the points A' and N^ is equal to 27°) we can 

 plot it in the plane of the rays from the normal in the direction opposite 

 to the incident ray (point B'). We next bring the tracing paper into its original 

 position. The point B' is now transferred to point B which also corresponds 

 to the direction of the ray after its reflection. The direction of the reflected 

 ray in our case is determined by the co-ordinates 185° and 30°. 



(b) To determine the direction of the refracted ray. The method is similar 

 to that used for the reflected ray, the only difference being that in this case 

 instead of plotting the angle of reflection, which is equal to the angle of inci- 

 dence, from the normal we plot the angle of refraction. The angle of refraction 

 is calculated from the angle of incidence and from the ratio of velocities 



— in the first and in the second layers according to Sn ell's equation: 



. . v^ 

 i2 1 = arc sm 112—=-. 



' ^1 



where : i^ i is the angle of refraction and ij g is the angle of incidence. 



By way of example let — = 1*5 in our case; then when ij^^ = 27° the 



angle of refraction ig^ will be equal to 43°. 



Since the refracted ray will be under the plane of the drawing we shall 

 construct on the grid the direction opposite to it. (As indicated above, we 

 shall for the sake of convenience denote the direction in such cases by a cross 

 and not by a point). For this purpose, as can be seen from the ray diagram 

 (see Fig. 3, b) it is sufficient to plot the angle of refraction from the normal 

 in the direction of the incident ray in the plane of the ray. The direction 

 of the refracted ray is denoted in Fig. 3, a by the point C If we rotate the 

 tracing paper into its original position we shall obtain from the point C the 

 co-ordinates of the refracted ray (43° and 47°). We must not forget, however, 

 that here we are dealing with a direction opposite to the direction of the 

 refracted ray, and therefore when we remove the co-ordinates we must take 

 the inverse azimuth. Then the direction of the refracted ray will be 223° 

 and 47°. 



(c) To determine the direction of a grazing ray. To obtain a grazing ray 

 the angle of refraction must be 90°. To determine the direction of the grazing 

 ray it is sufficient to plot an angle of 90° from the normal in the plane of the 

 ray and having restored the tracing paper to its original position to 

 take the co-ordinates of the grazing ray from the net (point K, Fig. 

 3, a). 



