66 OPTICAL PRINCIPLES OF THE MICROSCOPE. 



ing to the same ratio; and to find the course of the emergent 

 ray, the sine of the angle of incidence must be multiplied by the 

 "index of refraction," which will give the sine of the angle of 

 refraction. ~Now when an emergent ray falls very obliquely^ pon 

 the surface, the refraction which it would sustain in passing 

 forth, .tending as it does to deflect it still farther from the per- 

 pendicular, 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 

 reflection will take place, whenever the product of the sine of the 

 angle of incidence, multiplied by the index of refraction, exceeds 

 the sine of 90, which is the radius of the circle ; and therefore 

 the " limiting angle," beyond which an oblique ray suffers in- 

 ternal reflection, varies for different substances in proportion to 

 their respective indices of refraction. Thus, the index of refrac- 

 tion 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 of that 

 angle, 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 ; whilst at the same time it 

 enables the optician to make most advantageous use of glass 

 Prisms for the purpose of reflection; the proportion of the light 

 which they throw back being much greater than that returned 

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

 reflected image being consequently higher. Such prisms are of 

 great value to the Microscopist for particular purposes, as will 

 hereafter appear ( 40, 41, 57, 60). 



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 pass- 

 ing through convex lenses, whereby their performance is rendered 

 more exact ( 10, 12). It is easily shown to be in accordance 

 with the laws of refraction already cited, that when a "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 perpendicu- 

 lar to each point of curvature. The central or axial ray, as it 

 coincides with the perpendicular, will undergo no refraction ; the 

 others will be bent from their original course in an increasing 

 degree, in proportion as they fall at a distance from the centre of 

 the lens; and the effect upon the whole will be such, that they 

 will be caused to meet at a point, called the focus, some distance 

 beyond the centre of curvature. This effect will not be materi- 



1 The reader may easily make evident to himself the internal reflection of water, by 

 nearly filling a wineglass 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. 



