Electron Wave Optics 21 



The de Broglie wavelength of 60 kev electrons, however, is, 

 as we have seen, about 0.05 A, i.e., roughly one hundred thousand 

 times shorter' than for visible light. It is therefore possible to 

 make the aperture angle one thousand times smaller than in light 

 microscopy, and still retain a roughly one hundred times better 

 resolution. This, in short, is what electron microscopy has done 

 up to the present. 



At the end of the previous chapter, it was mentioned that the 

 reduction of the aperture would have been insufficient by itself 

 to eliminate the chromatic error, and that the great progress of 

 electron microscopy was achieved by using monochromatic 

 illumination. We can give now a more precise meaning to this 

 concept which we introduced in geometrical optics on the basis 

 of the different refrangibility of electrons of different velocities. 

 In a beam of average energy V ev, in which electrons of energies 

 differing by AV ev are present, the degree of inhomogeneity of 

 wavelength can be expressed by the fraction 



^=-^ (17) 



A 2V ^ ^ 



This follows from equation (13). The same applies also if the 

 voltage fluctuates by AV. In modern electron microscopes this 

 has been reduced to less than 1 part in 25,000 or even 50,000, so 

 that the de Broglie wavelength varies only by 0.004—0.002 per 

 cent. To appreciate this, we may consider that in optics the 

 sodium lamp is considered as a good monochromatic source. The 

 two D-lines of the sodium spectrum differ by about 0.1 per cent 

 in wavelength, which is fifty to one hundred times more than 

 the corresponding value in a good electron microscope. 



It is perhaps more appropriate to base the comparison on the 

 variation of refractive indices in the two cases. A good measure 

 of this is the relative dispersion 



A dn 

 n dX 



In electron optics A Is inversely proportional to VV, and thus to 



