170 OPTICAL PRINCIPLES. 



the incident ray ib with the perpendicular^, is equal 

 to the angle p b r, formed by the reflected ray b r 

 with the perpendicular p b. 



If the body upon the surface of which the rays are 

 incident be transparent, some of the rays will be re- 

 fracted and will pass through it, whilst others will be 

 reflected. The proportion of those reflected is small- 

 est when the rays are incident perpendicularly to the 

 surface; but this increases as the incident rays be- 

 come more oblique, i. e. as the angle of incidence be- 

 comes greater, although at no degree of obliquity are 

 the whole of the rays reflected. The case is different, 

 however, with those rays which enter the substance 

 and impinge upon its inner or second surface; for 

 these at a particular angle of incidence undergo total 

 reflexion, so that none of the rays are transmitted at 

 the second surface. The angle of total reflexion is 

 constant for the same medium, but different for dif- 

 ferent media : thus in crown glass it is equal to about 

 40, in flint-glass 38, &c. ; and this internal reflexion 

 from the second surface of transparent media is more 

 perfect than that occurring at the surface of opake 

 reflecting surfaces or mirrors. 



If the reflecting surface be concave, as in PL XII. 

 fig. 4, parallel rays will be reflected to a focus , nearer 

 the mirror than the centre of its curvature b, and this 

 focus is called the principal focus; while diverging 

 rays are brought to a focus nearer the centre of cur- 

 vature; and converging rays form a focus further 

 from the centre of curvature. 



Lenses. In most instances, as far as the microscope 

 is concerned, the surfaces of the glass through which 

 the rays of light are transmitted are not plane or flat, 

 but curved being either convex or concave, and be- 

 longing to convex or concave lenses. In considering 

 the course of rays through curved surfaces, the re- 

 fraction may be viewed as taking place at a plane 

 surface forming a tangent at the point of incidence of 



