BRIGHTNESS. 



259 



case, as is readily seen from the construction, the peripheral 

 pencils are cut off wholly or in part, while the middle ones pass 

 through unaffected. Such diaphragms therefore determine the 

 size of the field of view, and diminish more especially the cones of 

 light which reach the retina from the peripheral points. 



2. BRIGHTNESS. 



If the optically effective cones of light wholly occupy the 

 aperture of the pupil, as is usually the case for the central object- 

 points, they evidently possess, after the last refraction by which 

 their point of convergence is moved to the distance of distinct 

 vision, the same angle of aperture as those pencils which are 

 received by the naked eye. The brightness of the virtual image is 

 in this case (disregarding the loss caused by reflexion or absorption) 

 nearly equal to unity i.e., the objects are seen through the simple 

 Microscope nearly as bright as with the naked eye. The resulting 

 brightness, as with the compound Microscope, is more accurately 

 expressed by the formula 



/ a> \ o 

 v = (--)*, 

 \pml 



where v denotes the brightness, co the angle of aperture of the system, 

 p the angle of aperture of the naked eye for a particular length of 

 sight, and m the coefficient of linear amplification for the same dis- 

 tance of vision. If p = 1, as is, for instance, the case with a sight 

 of 172 mm., and the aperture of the pupil is 3 mm., the above 



expression may be simplified into ( \ 2 , if unity is taken as the 



\ wi / 



standard. Since the coefficients of amplification, calculating the 

 distance of vision from the posterior focal point, are in the same 

 ratio as the tangents of the half -angles of aperture (as both are in 

 inverse ratio to the focal length), it follows that the brightness 

 is the less the higher the amplification. A few examples in which 

 the corresponding values of co and m are placed side by side may 

 perhaps elucidate this decrease. 



