ILLUMINATION BY TRANSMITTED LIGHT. 



105 



element of the reflecting surface will therefore emit light corre- 

 sponding with the directions in which it is incident. If we dis- 

 regard the very small differences of loss which the rays reflected at 

 unequal angles undergo, the mirror will act with regard to the 

 object-plane of the Microscope precisely as a self-luminous sur- 

 face, each surface-element acting as a self-luminous point. *In 

 this case it is quite immaterial whether the mirror is plane, 

 concave, or convex, since the luminous power of the separate 

 surface-elements is not dependent on their inclination to the optic 

 axis, consequently the brightness of the whole mirror surface is 

 the same, whether this inclination varies from element to element 

 or remains constant. If a I represents the diaphragm, any surface- 

 element whatever of the object-plane p (Fig. 4)3) is, therefore, 

 illuminated by rays which proceed from the points of the mirror 

 -surface between m and n. Of the whole 

 cone of light diverging upwards, which each 

 of these points emits (in the Fig. indicated 

 for the point o), only an infinitely narrow 

 part co-operates, whose base is p. The in- 

 tensity of the illumination is, consequently, 

 so far as the mirror surface is sufficiently 

 extended, limited by the diaphragm a b, 

 which also limits the aperture of the in- 

 cident cone of light m p n on it. The dis- 

 tance of the mirror surface from the object 

 is immaterial ; for although the brightness 

 of a surface-element varies with the square 

 of the distance, the quantity of light varies 

 in the same proportion. The total quantity 

 of light is the same in either case. 



It follows, that a concave mirror will illuminate the object- 

 plane equally well, whether its focus lies in the plane itself or 

 not, on the supposition that its surface exceeds the limit deter- 

 mined by the diaphragm. For since the curvature of the mirror, 

 as above shown, is entirely without influence, the position of its 

 focal point has no optical importance. 



Let us now consider how the condition of an unlimited and 

 equally luminous source of light is practically fulfilled (by un- 

 limited we mean exceeding the limits determined by the dia- 

 phragm). In order to satisfy the above condition at least approxi- 



FIG. 43. 



