. Physiological optics : being an essay contributed to the American encyclopedia of ophthalmology . gives riseto concentric dark rings. The first minimum, as proven by Neumann,occurs when the angle of diffraction is such that Asin $ == — (Ill) P From equation II, r = y A • f or S, the diameter, equals 2VA ? f. Sincethe arc divided by the angle in radians is always equal to the radius,then, from equation III, A p 3 = - = (IV) $ 108 PHYSIOLOGICAL OPTICS since 82 =4A • f, then 8 * 8 = 4A • f and a substitution of the value of 8just deduced gives the equation A-f8 = If, then, p is
. Physiological optics : being an essay contributed to the American encyclopedia of ophthalmology . gives riseto concentric dark rings. The first minimum, as proven by Neumann,occurs when the angle of diffraction is such that Asin $ == — (Ill) P From equation II, r = y A • f or S, the diameter, equals 2VA ? f. Sincethe arc divided by the angle in radians is always equal to the radius,then, from equation III, A p 3 = - = (IV) $ 108 PHYSIOLOGICAL OPTICS since 82 =4A • f, then 8 * 8 = 4A • f and a substitution of the value of 8just deduced gives the equation A-f8 = If, then, p is the diameter of the aperture of the refracting system, /the position of the image produced by the same, A the wave-length oflight, the diameter of the mean diffusion circle, 8, is given by theexpression A-f 8 = (V). Taking A as %ooo mm- as the average wave-length and / of the eye equalto 20 mms.; expression (V) reduces to 1 8 = —. P If, then, the smallest pupillary diameter is taken as 2 mms., 8 = This size of the diffusion circle corresponds to a visual angle. Fig. 48.—Effect of a Stenopaie Opening. of 2 minutes and 6 seconds. Since the minimum visual angle separatingtwo points is usually taken as 1 minute, it can be readily seen thatthe diffraction produced by very narrow pupils must influence theacuteness of vision. The effects of a narrow stenopaie opening upon the size of retinalimages in various refractive conditions can be seen from an inspectionof Fig. 48. Let DF be a line object and df its retinal image which weconstruct by tracing the straight lines passing through the nodalpoint n. H indicates the position of the retina in an hyperopic eye,E of an emmetropic and M of a myopic eye. Place in front of the 109 8 PHYSIOLOGICAL OPTICS eye a screen A, perforated at the point P, situated on the axis. Theonly rays proceeding from F which can, under these conditions, enterthe eye is the ray FP, with the result that, in the hyperopic eye, theim
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