Theory of Illuminating Apparatus. By Dr. H. E. Fripp. 527 



of the perception of light. When looking through the Microscope 

 at a given luminous surface (field of vision), the intensity of light 

 transferred to the retina depends upon the conditions of its trans- 

 mission. The arithmetical expression of this intensity is found 

 in the ratio which the light cast on the retina by the Microscope 

 bears to that cast on an equal surface of the retina when the 

 same luminous surface is viewed by the unarmed eye. Professors 

 Nageli and Schwendener give in their book an exposition of this 

 subject, of which the following is an abstract: — The intensity of 

 light cast on the retina when a given luminous surface is viewed 

 by the unarmed eye does not vary with the varying distance of the 

 eye from the light, because the image formed on the retina becomes 

 larger or smaller in exact proportion with the increase or diminu- 

 tion of the angular spread of the pencils emitted from each point of 

 the object viewed. One might suppose that the same relation would 

 continue when objects were viewed through the Microscope, that is 

 to say, that the amplification of the Microscope image would rise 

 and fall in corresponding ratio with the magnitude of the hght- 

 cone incident on the objective. If this were so, we should see every 

 object as bright in the Microscope as with the naked eye. That is, 

 the intensity of light (Lichtstarke) of the Microscope would equal 

 unity. But the diameter of the Microscope image (and therefore 

 also of the retinal image) increases with the rise of amplification in 

 vastly greater ratio than does the angular spread of the light-cone 

 incident from the object and transmitted by the objective to the eye. 

 In vision with the naked eye, taking the pupd aperture = ^V 

 or xV inch, and the distance of clear vision =10 inches, the angu- 

 lar divergence of the pencil may be about half a degree. In vision 

 through the Microscope, on the contrary, it may amount to 90^ or 

 100" or over, according to the construction of the objective and its 

 magnifying power. In this case the amount of light entering the 

 eye through the Microscope from every point of the fieU is greater 

 than the amount which the unarmed eye takes in the ratio of 

 10 0^ to (hY or 200^ : 1. But this light is distributed over a retmal 

 surface larger than that occupied by the retinal image of the object 

 seen by the unarmed eye in proportion of the square of the Hnear 

 amplification, which we will call ni^. The resulting brightness of 



9QQ2 



field (which we will call v) is therefore represented hj v = —^' 



or, generalizing this formula, and setting &> for the angular aperture 



of the objective, and i for that of the pupil, then v = f - | . Hence 



the light intensity is = unity when m = 2(o, but less than unity 

 when 7/1 > 2a), which is the common case. Here it is assumed as 

 understood that the incident light oone is large enough to fill the 

 whole aperture of the objective, a condition seldom realized. In 



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