THE SENSE OF SIGHT. 655 



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, / (in 

 Fig. 316 a b), may now be easily calculated, when the size of the object, O 

 (in Fig. 316 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: a b =f N:N g,orab= A N g ; 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 

 nodal point of the eye, determines the size of the image; for if a line be 

 drawn from both the upper and lower ends of an object through this nodal 

 point, it is clear that the images of the respective points must lie on these 

 two rays where they intersect the retina. The distance of this nodal point 

 from the retina is 15.498 mm. It is clear, therefore, that the size of the 

 object is to the size of the image, as the distance of the object from the 

 nodal point is to the distance of the 

 nodal point from the retina; or, in 

 other words, to find the size of the 

 retinal image : multiply the diameter 

 of the object by 15.5 mm. and divide *r 

 by the distance of the object from 

 the eye. 



The Visual An HP _ Thevimial FlG ' 3i5- DRAWING DESIGNED TO SHOW 

 isuai Angle. e visual HOW THE VISUAL ANGLE ^ SlZE OF RETINAL 



angle IS defined as the angle formed IMAGE VARIES WITH THE DISTANCE OF AN 



by the intersection of two lines OBJECT OF GIVEN SIZE. For the distant position 



i f ,-1 , r of A-B the visual ancle is a; for the near 



drawn from the extremities of an position (dotted lines) (From stewar ^ 

 object to the nodal point of the eye. 



Beyond the nodal point, however, the lines again diverge and form an in- 

 verted or reversed image of the object on the retina. The size of the 

 visual angle increases with the nearness and decreases with the remote- 

 ness of the object; the retinal image correspondingly increases and de- 

 creases in size. These facts will become apparent from an examination of 

 Fig. 315. As the size of the retinal image diminishes when the visual angle 

 diminishes either as a result of the removal of a given object from the eye, or 

 of a diminution of the size of the object, there comes a limit in the size of the 

 visual angle, beyond which it is impossible to see the two end points (A and B) 

 of the object separately. When this limit is reached the size of the angle ex- 

 pressed in degrees of the circle, may be determined if the distance between 

 the two points and their distance from the eye be known. Thus it has been 

 experimentally determined that at a distance of 5 meters, the smallest object or 

 the smallest interval between two points which permits the eye to distinguish 



