828 



PRELIMINARY DIOPTRIC CONSIDERATIONS. 



have the same optical axis, such a system may be represented by two surfaces 

 having equal indices of refraction, separated by a definite distance. The rays 

 that fall on the first surface are not refracted by it, but are only displaced laterally 

 and run parallel to their original direction as far as the second surface. The 

 refraction takes place at this point, and in the same way as previously constructed: 

 that is as if only one refracting surface were present. For this calculation the 

 indices of refraction of the media, the radii of the refracting surfaces, and finally 

 the distance between these surfaces must be known : but this subject cannot be 

 discussed in any further detail here. The refracted ray is constructed in the 

 following manner: Let a b (Fig. 278, I) represent the optic axis, H the first 

 principal focus determined by calculation, h h the first principal plane, H t 

 the second focal point, hj hj the second principal plane, k the first nodal point, 

 k x the second nodal point, F the second principal focus, and F t F x the second 

 focal plane. Let m n be the direction of the incident ray; what is the direction 

 of the refracted ray? 



FIG 278. 



Construction: Displace the ray m n parallel with itself as m, n,, to the second 

 principal plane. Now, draw the line p k lf parallel to m x n. According to rule 

 2, pki and m, n must intersect at a point of the plane F F,. As p k, passes 

 through unrefracted, the ray from n x must likewise pass through r; and n, r is 

 therefore the direction of the refracted ray. 



Construction of the Image of a Point. Let o (Fig. 278, II) represent a point 

 31 light; where is the image of this point in the last medium? Draw from o the 

 axial ray o k, and make o x parallel to a b. Displace both rays parallel to them- 

 selves to the second principal plane: then draw mk, parallel to o k, and prolong 

 ?J + U ^ my parall r el to a b P asses through F; m k lf as the axial ray, is not 

 The image of the point n will be found at the point of intersection 

 of the prolonged rays n F and m k a (at O) . 



These constructions are not applicable to objects that are at some distance 

 the optical axis. For such a condition the eye is more advantageously 

 ructed than a camera obscura (being periscopic), because its surface of pro- 

 is a hemisphere, and consequently the images are sharper in its lateral 

 portions than would be possible on a flat surface. 



