40 PHYSICAL ASPECTS OF VISION 



about 500 rods. The amount of light needed for vision can be estimated 

 from the fact that stars of the 8th magnitude are visible, corresponding 

 to about 10 -9 erg/sec. In the laboratory setup, even less energy was 

 needed for detection. 



The subjects were able to detect light of wavelength 510 mp whose 

 intensity corresponded to about 10~ 10 energy units (ergs) incident on 

 the eye. This corresponds to about 100 photons. This energy has to be 

 corrected for the various reflections and absorptions experienced by 

 photons before they reach the retina and are absorbed. At the cornea 

 about 5% is reflected, leaving 95 photons to continue. Half of these are 

 absorbed in the humors of the eye, leaving about 45 photons. Eighty 

 percent of these are absorbed in the nonsensitive portions of the retinal 

 structure, leaving about 10 photons to be absorbed for this barely de- 

 tectable flash. 



In the actual experimental situation, it was found that light of a 

 particular intensity could always be seen. But when a slightly lower 

 intensity was used, the subject was always able to see the flash in a 

 certain percentage of cases. That is, for an intensity which can always 

 be seen, one cannot be found just slightly lower which is never seen. 

 Therefore, for each subject, that intensity which was seen 60% of the 

 time was arbitrarily taken as the threshold for that particular run. 

 There were variations from individual to individual, and even the same 

 person exhibited a day-to-day variation. In the experiments being dis- 

 cussed, seven subjects were studied, and the range for threshold seeing 

 was 2.1 to 5.7 X 10 -10 erg. One particular subject had a range of 4.83 to 

 5.68 X 10- 10 erg. 



At a wavelength of 510 mfi, the energy of a quantum is 3.89 X 10 -12 

 erg. Thus, the actual range in photons is from 



2.1 X 10- 10 5.7 X 10 -10 



to 



3.89 X IO-12 3.89 X IO-12 



which is 54 to 158 photons. Since about 10% of the photons get through 

 to the retina, the number of photons needed for threshold sensitivity is 

 5 to 16. 



We have 5 to 16 photons falling on 500 rods. On each rod, therefore, 

 there is an average (taking the 5-photon number for calculating pur- 

 poses) of 1 photon per 100 rods, or a chance of 0.01 that any one rod 

 received a photon. The chance that 2 photons will fall on the same rod is 

 then approximately 0.01 X 0.01 or 0.0001 — one chance in 10,000. Since 

 a total of only 5 photons reaches the rods, it is highly improbable that 

 two photons per rod are needed to produce a response. Thus, one photon 

 must react with one rod, affecting one molecule of the visual pigment, 



