356 Lord Rayleigh on the Accuracy of Focus 



It appears that the linear accuracy required is the same 

 whatever the absolute aperture of the object-glass may be, 

 provided that the ratio of aperture to focal length be pre- 

 served. 



In some trials that I have made the diameter of the object- 

 glass was 1J inch, and the focal length 12 inches. Taking 

 X= 4Q,o 00 inch, we get from (3) 



S/< -0115 inch, 



a result which corresponded very well with observation. The 

 instruments employed were the collimator and telescope of a 

 spectrometer, the object under examination being a slit backed 

 with a soda-flame. A high-power eye-piece was used, and 

 the telescope was adjusted until the edge of the slit and the 

 wire in the eye-piece were seen well defined together. The 

 instrument was unprovided with an easy focusing motion, 

 so that it was not possible to try backwards and forwards 

 conveniently. In this way the setting corresponded more 

 closely to the suppositions of theory than if it were the result 

 of comparisons between appearances at equal distances within 

 and without the point chosen. It will be understood that 

 there is no theoretical limit to the accuracy with which a 

 focal point may be ultimately determined, if the lenses are 

 good, and observations are multiplied with suitable precautions 

 to avoid asymmetry. 



In ten settings the extreme difference was only *02 inch - 

 showing that a displacement of 01 inch from the true focal 

 point was just recognizable. 



By using various coloured flames, or by thro win o- a spec- 

 trum upon the slit of the apparatus, we may determine the 

 focal length for different kinds of light. With proper achro- 

 matic lenses the differences should be pretty small the 

 minimum focal length corresponding to the yellow- oreen 

 rays. It so happens that my instrument is far from properly 

 compensated, and gives a fair primary spectrum, so that the 

 difference of focus for yellow and green is very easily recog- 

 nized. In the case of a single lens this method would oive 

 the dispersive power of the glass with fair accuracy. ^By 

 comparison with the theory of the resolving power of prisms 

 we see that the dispersion is about as favourably determined 

 with a lens as with a prism of equal thickness. In either 

 case a change of index such that 8/jl . t = ±\ leaves the phase 

 agreement nearly unaltered at the original points ; but in 

 other respects the circumstances are probably rather more 

 favourable in the case of the prism. 



It is generally considered that the most accurate way of 



