826 



PRELIMINARY DIOPTRIC CONSIDERATIONS. 



(more exactly the index of refraction is 1.535). The sines of the angles of inci- 

 dence and refraction are in the same ratio as the velocities with which the rays 

 of light pass through the two media. 



The refracted ray is, therefore, easily constructed, if the indices of refraction 

 are known. Example: Let L (Fig. 274) represent the air, G a denser medium 

 (glass), with a spherical surface, x y, the center of which is at m; P O represents 

 the oblique incident ray; m Z is then the axis of incidence, and the angle i the 

 angle of incidence. Let the index of refraction be |; what is the direction of 

 the refracted ray? 



Construction. Draw a circle of any radius, with its center at O; then from a 

 draw a line a b perpendicular to the axis of incidence m Z ; then a b is the sine of 

 the angle of incidence, i. Divide the line a b into 3 equal parts, and prolong it a 

 distance equal to two of these parts, that is to P. Now, draw from P the line P n, 

 parallel to m Z. Then the line joining the two points O and n is the direction of 

 the refracted ray. If the line n s is drawn perpendicular to m Z, n s = b P. Further, 

 ns = the sine of the angle r. According to the construction, ab : sn (or : b P) 

 = 3 : 2, or sine i : sine r = . 



Optical Cardinal Points of a Simple Collecting System. Two refractive media 

 (Fig. 275, L and G), which are separated from each other by a spherical surface 

 (a b) , form a simple collecting system. From a knowledge of certain properties 

 of such a system, it is easy to construct an incident ray from the first medium (L) 

 striking the separating surface obliquely, and also its direction in the second 



FIG. 275. 



medium G, as well as to determine, from the position of a luminous point in the 

 first medium, the position of its image in the second medium. The requisite proper- 

 ties and points of such a simple collecting system are as follows: 



L (Fig. 275) is the first, and Gthe second medium; a b is the spherical surface 

 separating them, and m its center of curvature. All radii drawn from m to ab 

 (m x, m n) are, of course, normal to the surface, so that all rays of light coming in 

 the direction of the radii, must pass through m without deviation. All such rays 

 are called axial rays; and m, their point of intersection, is the nodal point. The 

 line that connects m with the vertex of the spherical surface (x) and is prolonged 

 in both directions is called the optical axis (O Q) . A plane (E F) erected perpen- 

 dicular to O Q at x is the principal plane, and x is its principal point. The follow- 

 ing facts have been determined: 



(i) All rays (from a to a 5 ) that fall upon a b and are parallel to each other and 



the optic axis in the first medium will be so deflected by the second medium 



that they are united at one point ( Pl ) in the latter. This point is called the second 



principal focus. A plane erected at this point perpendicular to O Q is called the 



second focal plane (C D). (2) All rays (from c to c 2 ) that are parallel to each 



rtner in the first medium, but not parallel to O Q, are reunited at a point in the 



second focal plane (r) at the intersection of the undeflected axial ray (c^m r) with 



us plane (the angle, however, that the rays from c to c 2 make with O Q must be 



i he converse of propositions i and 2 is also true: the rays diverging 



trom Pl , and directed toward a b, continue through the first medium parallel to 



