110 



THEORY OF THE MICROSCOPE 



the detail that has already been defined in the real image formed by the objective, 

 and that any defects in this image are exaggerated by the magnification of the 

 eyepiece. 



2. Spherical aberration Coma. 



As it is of supreme importance to obtain the most perfect objective possible, 

 some of the defects in the image formed by a simple convex lens when homo- 

 geneous light (light of one specific wave-length, i.e. of one colour) is used 

 will be considered first and their correction explained, and then the defects 

 in the image due to chromatic aberration when ordinary white light is used 

 will be very briefly referred to. 



The defects in the image formed by a simple convex lens when homogeneous 

 light is the illuminant are two : spherical aberration and coma. 



Suppose a small bright point P (fig. 104) to lie on the axis of a biconvex lens ; 

 now, although the small axial cone converges fairly accurately to the conjugate 

 focus Q, the eccentric rays PL, PL' converge to a nearer focus Q'. The peripheral 

 parts of a lens refract light more strongly than the central parts, and hence the 

 image of the point P will be blurred on account of spherical aberration. The only 

 way of getting over this difficulty known to the early opticians was to cut off the 

 peripheral rays by means of a diaphragm, but this, of course, very seriously diminished 

 the brightness of the image. 



Now take the case where a point P 7 (fig. 105) does not lie on the axis of the lens ; 



FIG. 104. 



FIG. 105. 



the image of P' will be indistinct for a reason which is somewhat similar to that given 

 in the former case, as will be evident from a glance at the figure. The centric pencil 

 will form a well-defined image at Q, but while the rays 1 and 2 will intersect at A 

 the rays 3 and 4 will intersect at C. Hence if a screen be placed in the position 

 QF a bright point will be seen at Q, which becomes an ill- defined flare 

 of light towards F l (fig. 106). The image somewhat resembles the tail 

 of a comet and the defect is therefore known as coma (KO/O/, hair of 

 the head, tail of a comet), and may be regarded as the spherical 

 aberration for object points not on the axis. 



These two defects, spherical aberration and coma, must therefore 

 be corrected before any definite distinct image can be formed by 

 an objective. An image free from these defects is known as an 

 aplanatic image (<x7r/\aijs, not wandering). The condition for 

 Fl Coma'-~ aplanatism can only be obtained in one way^-the lenses must 

 satisfy what is known as Abbe's sine law. 



The sine condition for aplanatism. Let C be the centre of the circle KAK' (fig. 107), 

 and let P be a point situated at a distance CP from the centre of the circle, such 



that f-^-rr- 



U-IV fJt 



. 9 



PC fi' 



i.e. the radius of the circle : the distance of the object to its centre 



: : the index of refraction of the first medium : the index of the second medium.. 



1 F, in this figure, is arbitrary and not the focus. 



2 In "primary" coma the angle formed by the tangents to the series of circles from, 

 the point Q in this figure is said to be 60. 



