4 OPTICAL PRINCIPLES OF THE MICROSCOPE. 



vacuum,* if its angle of incidence exceed 48° 28', since the sine 

 hh' of that angle, h o c', multiplied by 1*336. equals the radius ; 

 and in like manner, the ' limiting angle ' for Flint-glass, its index 

 of refraction being 1'60, is 38° 41'. — This fact imposes certain 

 limits upon the performance of microscopic Lenses, since of the 

 rays which would otherwise pass out from glass into air, all 

 the more oblique are kept back ; whilst, on the other hand, it 

 enables the Optician to make most advantageous use of glass 

 Prisms for the purpose of reflexion, the proportion of the light 

 which they throw back being much larger than that returned 

 from the best polished metallic surfaces, and the brilliancy of the 

 reflected image being consequently greater. Such Prisms are of 

 great value to the Microscopist for particular purposes, as will 

 hereafter appear. (§§26-29.) 



3. The Lenses employed in the construction of Microscopes are 

 chiefly convex ; those of the opposite kind, or concave, being only 

 used to make certain modifications in the course of the rays passing 

 through convex lenses, whereby their performance is rendered more 

 exact (§§ 10, 12). — It is easily shown to be in accordance with the 



Parallel rays, falling on a platw-convex Lens, brought to a focus 

 at the distance of the diameter of its sphere of curvature ; and 

 conversely, rays diverging from that point, rendered parallel. 



laws of refraction already cited, that when a i pencil ' of parallel 

 rays, passing through air, impinges upon a convex surface of glass, 

 the rays will be made to converge ; for they will be bent towards 

 the centre of the circle, the radius being the perpendicular to each 

 point of curvature. The central or axial ray, as it coincides with 



* The reader may easily make evident to himself the internal reflection 

 of Water, by nearly filling a wine-glass with water, and holding it at a 

 higher level than his eye, so that he sees the surface of the fluid obliquely 

 from beneath ; no object held above the water will then be visible through 

 it, if the eye be placed beyond the limiting angle ; whilst the surface 

 itself will appear as if silvered, through its reflecting back to the eye the 

 light which falls upon it from beneath. 



