32 Light and the Eye \1 : 2 



it impossible to avoid the conclusion that light is a wave motion repre- 

 sented to a sufficient approximation by rays only in limited circum- 

 stances. The limitations are sufficiently broad to allow the use of 

 geometrical optics in many visual problems. 



The wave nature of light has two very important consequences for the 

 sensation of vision. The first is that there is a theoretical limit to the 

 resolution of any lens system, including the eye; that is, there is a mini- 

 mum separation of two points whose images are resolvable. Figure 2 

 shows the diffraction patterns of the light originating from two point 

 light sources. If one computes the dimensions of the diffraction patterns 

 of the light originating at the two points and asks that the central 

 maximum of one coincide with the first minimum of the second, one 

 finds that the angular separation of the lines from the lens center to 

 the two points is given by 



9-1™ ' (4) 



a 



where A is the wavelength of the light and a is the radius of the aperture 

 of the lens. It is often assumed that this is about the minimum separation 

 at which two points can be distinguished. The reciprocal of 6 in minutes 

 of arc is called the resolving power. Actually, trained microscopists 

 and spectroscopists resolve slightly smaller angles than the one computed 

 by the formula above. (This formula was first developed by Lord 

 Rayleigh; it is often called the Rayleigh criterion.) 



In addition to its use in predicting resolving power, the wave nature 

 of light is necessary to discuss color vision. If light of a narrow wave- 

 length band is present, it is said to be monochromatic; that is, it gives 

 the sensation of a single color. Only about one octave (that is, a factor 

 of two in the frequency) is visible to humans. In wavelength terms, 

 the visible spectrum runs from about 760 mfi (red) down to about 

 380 OT/u, (violet), although the exact limits quoted by different experi- 

 menters vary. One octave seems a narrow band when compared with 

 the sense of hearing where musical tones are audible in at least nine 

 octaves. The resolution of different wavelengths by the eye is much 

 poorer than the sharp tone discrimination of the ear. Combinations of 

 different wavelengths of light produce complex color sensations because 

 the eye does not analyze frequencies in any fashion analogous to that of 

 the ear. 



Light waves are not elastic disturbances. A number of different 

 types of experiments have left no doubt that light waves are electro- 

 magnetic waves. Two of these experiments will be mentioned here. 

 First, one can compute on theoretical grounds that an electromagnetic 

 wave should be transverse and have a velocity which can be determined 



