OPTICAL PRINCIPLES OF THE MICROSCOPE. > 



angle of refraction. And thus, when an emergent ray falls very obliquely 

 upon the surface of the denser medium, the refraction which it would 

 sustain in passing forth into the rarer medium, tending as it does to 

 deflect it still farther from the perpendicular, becomes so great that the ray 

 cannot pass out at all, and is reflected back from the plane which separates 

 the two media, into the one from which it was emerging. This internal 



beyond which an oblique ray suffers internal reflection, varies for differ- 

 ent substances in proportion to their respective indices of refraction. 

 Thus, the index of refraction of Water being 1.336, no ray can pass out 

 of it into a vacuum, 1 if its angle of incidence exceed 48 28', since the 

 sine h li' 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 advan- 

 tageous use of glass Prisms for the purpose of reflection, 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. ( 33- 

 38.) 



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 ( 11, 13). It 

 is easily shown to be in accordance with the laws of refraction already 

 cited, that when a bundle of parallel rays, passing through air, impinges 

 upon a spherical surface of glass, these rays will be made to converge. 

 For the perpendicular to every point of that surface is the radius drawn 

 from the centre of the sphere to that point, and prolonged through it; so 

 that, whilst any ray which coincides with the radial perpendicular will go 

 on without change* in its course towards the centre of the sphere; every 

 ray which falls upon the spherical surface at an inclination to its pro- 

 longed radius undergoes refraction in a degree proportionate (as already 

 explained) to that inclination. And the effect upon the whole bundle- 

 will be such, that its rays will be caused to meet at a point, called the 

 focus, some distance beyond the centre of curvature. This effect will be; 

 somewhat modified by the passage of the rays into air again through a, 

 plane surface of glass, perpendicular to the axial ray (Fig. 2); and a lens 

 of this description, called & plano-convex lens, will hereafter be shown to 

 possess properties which render it very useful in the construction of 

 Microscopes. But if, instead of passing through a plane surface, the 

 rays re-enter the air through a second convex surface, turned in the oppo- 

 site direction, as in a double-convex lens, they will be made to converge 



1 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. 



