of Brightness of Images. 219 



from A if not stopped) in pencils of magnitude co. The 

 justness of this measure is obvious from the fact that if we 

 halve either A or to we shall halve the quantity of light that 

 will come into consideration. 



When the small area A is taken on the surface of the object 

 itself, the value of the expression (11) is called the intrinsic 

 brightness of the object. 



In the case of the two small areas which we have been dis- 

 cussing, let q denote the quantity of light sent by A 2 on the 

 road to A v If none of it is lost on the road, it all reaches A x ; 

 thus the same quantity of light which leaves A 2 in pencils of 

 angle co 2 reaches Aj in pencils of angle e^. Let I 2 denote the 

 intrinsic brightness of A 2 , and I its apparent brightness as seen 

 from A l ; then 



I=-JL_ = £© -JL = (&Y.J- = f^Yl 2 . . (12) 



A^ -A-iCOi A 2 w 2 \/x 2 / A 2 &> 2 \fx, 2 y 



By supposing \jl 2 equal to y^ we obtain the following 

 theorem. If the eye and the object are in media of the same 

 index, and no light is stopped on its way from, the object to the 

 eye, the apparent brightness is equal to the intrinsic brightness, 

 notwithstanding any refractions or total reflexions that the rays 

 may have undergone beticeen the object and the eye. 



If light is lost on the way, the above expression for the 

 apparent brightness must be multiplied by a coefficient k less 

 than unity, which, by well-established laws of Optics, is the 

 same for rays going from A 2 to A x as for those going from 

 Aj to A 2 (for the same kind of light). If I 2 and Ij are the 

 intrinsic brightnesses of the two areas, their apparent bright- 

 nesses when each is seen from the other will be 



C) 1 * ™ dk (%P' (13) 



When an observer sees the area A 2 , the pupil of his eye may 

 be taken as the area A l ; the foregoing computations of appa- 

 rent brightness accordingly assume that all parts of the pupil 

 receive rays from every part of A 2 . If part of the pupil be 

 covered, the apparent brightness of the object will be dimi- 

 nished ; and a similar diminution will occur when the rays 

 from the object are collected into a beam of such small section 

 as not to fill the pupil. This is the cause of the falling off of 

 light which is observed in the use of high magnifying-powers 

 with optical instruments. 



In the case of light sent out obliquely from the surface of 

 an object, the above investigations will remain applicable if 



