THE SENSE OF SIGHT 



707 



B 



FIG. 295. DRAWING DESIGNED TO SHOW 

 HOW THE VISUAL ANGLE AND SIZE OF RETINAL 

 IMAGE VARIES WITH THE DISTANCE OF AN 

 OBJECT OF GIVEN SIZE. For the distant position 

 of A-B the visual angle is a; for the near 

 position (dotted lines) ft. (From Stewart.) 



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 '<J^_ A X XA 



other words, to find the size of the 

 retinal image : multiply the diameter 

 of the object by 15.5 mm. and divide 

 by the distance of the object from 

 the eye. 



The Visual Angle. The visual 

 angle is defined as the angle formed 

 by the intersection of two lines 

 drawn from the extremities of an 

 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. 295. 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 

 them as such, is about 1.454 mm. Lines drawn from the extremities of 

 such an object or interval, to the nodal point, subtend an angle of 60 seconds. 1 

 Beyond this the two points are indistinguishable. In other words the 

 emmetropic eye possesses the power of distinguishing the correspondingly 



1 The size of the visual angle, under which an object of this size and situated at a distance 

 of 5 meters is distinctly seen, can be determined from the following Fig. 296, in which A B represents 



the size of the object i .454 mm. ; 

 N, the nodal point; CN, the 

 line which bisects the object, 

 represents the distance of the 

 object from the nodal point; 

 a, the visual angle subtended 

 and whose value it is desired 

 to know, and b one-half of the 

 angle a. By trigonometry the 



size of the angle a can be de- 



FIG. 206. FIGURE SHOWING THE METHOD OF OBTAINING termined in the following way: 

 THE VISUAL ANGLE EXPRESSED IN DEGREES OR FRACTION one-half the size of the object 

 OF A DEGREE OF AN ARC. A B, is divided by its distance 



from the nodal point; the quo- 

 tient is the tangent of half the angle. Thus 0.727 -* 5000 =-0.0001454. By reference to tables of 

 natural tangents, it will be found that the angle or fraction of the circle corresponding to this 

 tangent is 30 seconds, and that therefore the whole angle is 60 seconds. 



