Theory of IllmninaUng ApiMratus. By Br. II. E. Fripp. 519 



where A B represents the plane mirror, C D the concave miiTor, 

 a — h, the aperture in a diaphragm below the stage, and p a point 

 in the focal plane of the object on which the Microscope is focussed, 

 that the lines p m, p n, form the limiting boundary of a con- 

 verging cone of light-rays reflected by either mirror. Assuming 

 that the mirror is large enough to occupy the base of this illumi- 

 nating cone, the intensity of illumination will vary with the size of 

 the aperture in the diaphragm. And it matters not whether the 

 mirror be nearer to or further from the point p, if only it be large 

 enough to subtend the base of the cone : for since the area of 

 reflecting surface increases with its distance from the point p, the 

 number of illuminating points compensates for diminished intensity 

 of Hght. If the diaphragm were removed, the face of the mirror 

 would form the base of the illuminating cone, and in proportion as 

 the mirror is brought nearer to the point p, will the angular 

 spread of this cone increase. 



It follows also, from the demonstration given with Fig. 3, 

 that the cone of light from the concave mirror, circumscribed by 

 the same diaphragm aperture, illuminates the point p) as well 

 (but no better) whether its focus falls exactly upon p, or not. As 

 the curve is without influence in this direction, so the position of 

 its focus has no optical significance. When the condition of un- 

 limited expanse of sky light is realized, the converging cone of the 

 plane mirror reflection has as good a claim to be considered " con- 

 densed " light as that of the concave mirror, or that of the collect- 

 ing lens. But when its surface does not afford a sufficiently large 

 base for a cone of light, which might act with real optical effect 

 through a given diaphragm aperture, it is then deficient: and 

 when it is sufficient for all effects the diaphragm has a special 

 function to fulfil in controlling by exclusion or admission the 

 amount of light requu'ed for each object according to the magnifying 

 power of the objective used. 



But in the next place, if we compare the outward course of the 

 lines (in Figs. 4, 5, 6), which represent the incidence of the respec- 

 tive cones of hght falling upon the two mirrors from the respective 

 Hght-sources, we find difierences which suggest reasons for the 

 selection of one or the other according to the particular circum- 

 stances of the case. 



If the Microscope be set up close to the window, and the mhror 

 towards a clear sky, the condition of an unlimited expanse of light- 

 source is fulfilled, provided the window- frame allows passage to all 

 rays of light included within the outlines of the cone traced by the 

 outermost rays incident upon the mirror to form the illumination. 

 Thus, if p m and p n represent the outlines of a luminous cone 

 touching the edges ah oi the diaphragm aperture and based on the 

 mirror A B, then the incidence is found by construction (in tracing 

 back the angle of incidence equal to that of reflection) at s and t 



