On the Theory of Optical Images, 1G7 



of #-rays. The production of diffuse reflexion by solid bodies 

 is very easily observed; but hitherto I have no clear evidence 

 of specular reflexion. Air unfortunately itself sets up dif- 

 fusion, behaving as a semi-opaque fluid. If ordinary expe- 

 riments on the reflexion of light had to be carried on in dense 

 smoke or in milky water,- a similar diffusion would interfere 

 with specular reflexion. In one set of experiments a V-tube 

 made of lead pipes set at right angles, and open at the bottom, 

 was used, the a-ray source being made to shine down one 

 limb, while a shielded photographic plate w r as placed at the 

 upper end of the other. The surfaces to reflect ^-rays were 

 placed at the open lower ends at 45° to the lines of incidence 

 and of presumed reflexion. Reflexion of a sort was indeed 

 obtained when surfaces of metal and of glass were placed 

 across the bottom of the tubes. But an effect was also 

 obtained even when nothing was placed across the open 

 bottom. It seems exceedingly doubtful whether true specular 

 reflexion has been observed in any case. 







XV. On the Theory of Optical Images, with Special Reference 

 to the Microscope. By Lokd Rayleigh, Sec. E. S* 



THE special subject of this paper has been treated from 

 two distinct points of view. In the work of Helmholtz f 

 the method followed is analogous to that which had long 

 been used in the theory of the telescope. It consists in 

 tracing the image representative of a mathematical point in the 

 object, the point being regarded as self-luminous. The limit 

 to definition depends upon the fact that owing to diffraction the 

 image thrown even b}' a perfect lens is not confined to a point, 

 but distends itself over a patch or disk of light of finite dia- 

 meter. Two points in the object can appear fully separated only 

 when the representative disks are nearly clear of one another. 

 The application to the microscope was traced by means of a 

 somewhat extended form of Lagrange's general optical 

 theorem, and the conclusion was reached that the smallest 

 resolvable distance e is given by 



e = |X/sina, (1) 



X being the wave-length in the medium where the object is 

 situated, and a the divergence-angle of the extreme ray (the 

 semi-angular aperture) in the same medium. If \ be the 

 wave-length in vacuum, 



X=V/*> (2) 



* Communicated by the Author. 

 t Pogg. Ann. Jubelband, 1874. 



