Professor A. E. Conrady contributed some *' Notes on 

 Microscopical Optics, " which were communicated by 

 Professor Alfred W. Porter, F.K.S. 



NOTES ON MICROSCOPICAL OPTICS. 

 By a. E. Conrady. 



It is manifestly impossible to give an exhaustive treatise on 

 microscopical optics in a short paper, but a brief indication of wnat 

 has been done and what is likely to be accomplished in the near 

 future may be acceptable. 



The resolving and defining power of the microscope depends 

 primarily on the high correction of spherical aberration in cones of 

 rays of very large angular aperture. The first approximation methods 

 which are useful in arriving at preliminary designs of telescope 

 objectives will only give rough indications of the required forms of 

 components even in the lower powers of microscope objectives, and 

 they are quite useless in the case of the higher powers. 



Exact trigonometrical ray-tracing must therefore form the founda- 

 tion of the designer's work. It is not, however, desirable to depend 

 entirely upon this method, for the real desideratum in every lens 

 system is that all the light from an object-point should reach the 

 image point along paths of the same optical length, and according 

 to the classical ITmit recommended by the late Lord Rayleigh, this 

 equality of optical paths should not be departed from to a greater 

 extent than J wave-length, say five one-millionth of an inch. It 

 used to be thought by practical opticians that this represented a 

 perfectly absurd and unattainable degree of perfection, but I showed 

 long ago (Monthly Notices R.A.S., April, 1905), that so far is this 

 from being true that the Rayleigh limit really represents a far 

 more generous allowance, in the ratio of about 4 to 1, than the 

 union of the geometrical rays within a " circle of confusion " equal 

 to the resolving power of an objective, which latter condition was 

 looked upon as practicable. Quite recently the fulfilment of the 

 Rayleigh condition in good telesco]}e and microscope cbjectives has 

 been put to the direct experimental proof by that valuable innova- 

 tion : the Hilger Lens-Interferometer. In the paper quoted above 

 I gave a trigonometrically exact method of detcrminitiy the phase- 

 relation in which rays arrive at a focus. I had used the method for 

 about 10 years at the time of its publication, and all my designs 

 of microscope objectives are based on its use : but up to the time when 

 I began lecturing at the Imperial College I was probably the only 

 designer who took advantage of this method, which is not only the 

 soundest from the theoretical point of view, but also by far the 

 easiest and quickest. As it gives the exact amount of spherical 



