JOURNAL 



OF THE 



WASHINGTON ACADEMY OF SCIENCES 



Vol. IV MARCH 19, 1914 No. 6 



PHYSICS. — The brightness of optical images. P. G. Nutting, 

 Eastman Kodak Research Laboratory. 



The relative brightness of an object and its image formed by a 

 lens may be calculated by certain well known formulae when the 

 relative aperture of the lens is small and the object distance great. 

 Experimental determinations of relative brightness have been 

 made but not with sufficient precision to permit of a satisfactory 

 deduction of the light lost during transmission through the lens. 



In this article are given first an extension of the theory to 

 lenses of all apertures and focal lengths and to all object distances. 

 A method is described of measuring relative illumination with a 

 precision as high as that reached in the best ordinary photometry. 

 Both investigations were initiated and carried out at the research 

 laboratory of the Eastman Company. The unabridged paper 

 (to appear elsewhere) contains the complete mathematical theory 

 and experimental data. 



The theoretical investigation leads to an expression for the 

 flux density I of radiant power, in watts per unit area, entering 

 the image, relative to that (7o) leaving the object. This expres- 

 sion is in terms of radius of effective aperture R of the lens, dis- 

 tance of object u and image v measured from the nodal point of 

 the lens. The formula is simplified if we substitute magnification 

 m for the ratio v/u of image distance to object distance, and in- 

 troduce the symbol a = R/F, the* ratio of the radius of effective 

 aperture to equivalent focal length F. The complete formula is 



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