114 BIOPHYSICAL CHARACTERISTICS OF THE EYE 



factor of only 10 million. Can this discrepancy be accounted for by a 

 variation in the size of the pupil? The total range in pupillary diameter 

 is from 2 to 8 mm, or a range in area from 1 to 16, the pupil adjusting 

 itself so as to maintain constant light energy on the retina. Appar- 

 ently, this is not a sufficient variation to account for the discrepancy. 

 A time element, however, is also involved when the retina is exposed 

 to the radiant energy. The time of the exposure, especially at threshold 

 vision, modifies the expected results. 



The time element of the retinal exposure can be obtained from some 

 data collected by Reeves [1918], which show that at low intensities the 

 product of time and threshold brightness, measured in millilamberts, is 

 only approximately constant. His data were obtained by using a 

 carefully calibrated focal plane shutter for determining the time of 

 exposure, when a 3 cm square test spot was placed at a distance of 

 35 cm. 



This result indicates that, the lower the intensity, the longer must 

 the image remain on the retina to produce a sensation of brightness, 

 and that a high intensity lingering for a short period of time does not 

 produce the same brightness effect as a low intensity lingering for a 

 long period of time. Hence the product of threshold by time should be 

 constant if the energy density on the retina is to remain constant. The 

 retina acts as if the radiant energy were integrated in some way to pro- 

 duce the threshold effect. Therefore brightness increases in proportion 

 as either the intensity or the time intervals are increased, and equal 

 brightness near the threshold is obtained if the product time-intensity 

 remains constant. That is, as duration is increased, intensity must be 

 decreased in order that the response remain at threshold value. 



This relation ceases to be effective if the time of stimulation is longer 

 than a critical duration of about 0.1 sec, as Reeves' data show in the 

 sudden change in values of threshold X time for values of time greater 

 than 0.160 sec. 



This fact is of importance in flashlight signaling. The blinker should 

 remain open for at least 0.1 sec in order to make the greatest possible 

 retinal impression. 



Energy Threshold 



If the energy entering the pupil is E ergs per second, it should be 

 proportional to the square of the radius (r) of the pupil, inversely pro- 

 portional to the square of the distance (D) of the test spot from the 

 observer, and directly proportional to the area (A) of the test spot 

 measured in square centimeters, to B its brightness in lamberts, and to 



