7 o6 TEXT-BOOK OF PHYSIOLOGY 



nodal point, which latter becomes the center of curvature of the single re- 

 fracting surface. The dimensions of this "reduced" eye are as follows (see 

 Fig. 293). From the anterior surface of the cornea, corresponding to the 

 principal plane H, to the nodal point N, 5.215 mm., from the anterior focal 

 point F v to the principal plane H, i.e., the anterior focal distance/, 15.498 

 mm.; from the principal plane H to the posterior focal point F 2 , i.e., the 

 posterior focal distance/", 20.713 mm.; the index of refraction is 1.3365. 

 There is thus substituted for the natural eye a single refracting surface with 

 a radius of curvature, r, of 5. 1 25 mm. In such an eye luminous rays emanat- 

 ing from the anterior focal point are parallel to the axis after refraction in 

 the interior of the eye. Also rays parallel to the axis before refraction unite 

 at the posterior focal point. 



By means of this reduced eye the construction of the refracted ray, the 

 various calculations as to the size of the image, the size of diffusion circles, 

 etc., are greatly facilitated: e.g., 



In Fig. 294 let A B represent an object. From A a pencil of rays falls 

 on the single refracting surface. One of the rays, the nodal ray, falling on 

 the surface perpendicularly, passes unrefracted through the single nodal point, 



FIG. 293. THE REDUCED EYE. FI G. 294. THE FORMATION OF AN IMAGE IN THE 



REDUCED EYE. 



N, to the posterior focal plane. The remaining rays, partially represented 

 in the figure, falling on this surface under varying degrees of incidence, 

 undergo corresponding degrees of refraction, by which they form a converg- 

 ing cone of rays which unite at a point situated on the nodal ray. These 

 two points, A, a, are known as conjugate foci. The same holds true for 

 a pencil of rays emanating from B or any other point of the object. 



The Size of the Retinal Image. The size of the retinal image, I (in 

 Fig. 294 a b), may now be easily calculated, when the size of the object, O 

 (in Fig. 294 A B ), and its distance, D, from the refracting surface with radius 

 of curvature, r, are known, by the following formula: 



0:I=D+r:f"-r. 

 For, as the triangles A N B and a N b are similar, we have 



A B: ab=fN:N g, or ab^~~~^ t - and therefore / = - 



Independent of the foregoing method, the size of the retinal image may be 

 calculated if it is remembered that the eye, like any optic system, has a point 

 of such a quality that a ray of light which before entering the eye was directed 

 toward it, after refraction continues as if it came from this point. In other 

 words, there is in the eye a point which allows a ray of light to pass unre- 

 fracted as would a pinhole instead of a lens. This point, termed the 



