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LXXXIX. Note on a possible Relationship between the Focal 

 Length of Microscope Objectives, and the number of Fringes seen 

 in Convergent Polarized Light. By F. Ian G. Rawlins*. 



IN connexion with a statement by Groth ('Optical Pro- 

 perties of Crystals,' Chapman & Hall, 1910), to the 

 effect that the number of interference fringes seen in crystals 

 by means of a microscope in convergent polarized light is a 

 function of the focal length of the objectives used, it was 

 considered of interest to investigate this — in as simple a way 

 as possible — with a view to determining whether such rela- 

 tionship was capable of exact mathematical expression: more 

 especially since inquiry into the literature of the subject 

 failed to show that this aspect of the question had received 

 attention. 



Three crystals were available for trial (quartz, tourmaline, 

 and mica), the approximate thicknesses being 5, 4, and 1mm. 

 respectively. It is clearly necessary to have sections of 

 unusual thickness, otherwise a sufficient number of obser- 

 vations cannot be made. Daylight was used together with 

 a red gelatine filter. The objectives were ordinary achro- 

 matic lenses, and the figures were viewed by means of a 

 supplementary Becke lens above the eyepiece. 



The following data were obtained : — 



Quartz. 



Tourmaline. 



Mica. 



Focal Length 



of Objective 



in mm. 



= F. 



No. of 

 Rings 



=N. 



Focal Length 



of Objective 



in mm. 



= F. 



No. of 

 Rings 



Focal Length 

 of Objective No. of 

 in mm. Rings 

 = F. =3S\ 



32 







32 



9 



16 1 



22 



2 



22 



2 



8 4 



16 



4 



16 



4 



4 7 



8 



8 



8 



11 





4 



11 



4 



16 





These results are plotted on the accompanying graph 

 (dotted-line curves), from which it will be seen that a fairly 

 smooth curve can be drawn through the points. Plotting 

 log F against log N was a failure in so far that a straight 

 line was not forthcoming. 



A trial was then made by taking for variables Jog e F 

 and N, and the points shown in solid lines were obtained. 

 It is apparent that straight lines can be drawn through these 

 * Communicated by the Author. 



