24 ELEMENTARY PRINCIPLES OF MICROSCOPICAL OPTICS 



traced, in the manner already indicated, through the aplanatic com- 

 bination, it will be found that the rays which before immergence 

 were diverging are by the refraction of the combination on emer- 

 gence rendered converging. Thus the ray F C meets H C at the 

 point C. The point C is called the conjugate focal point of A, and 

 wherever there is a focal point there will be an image. Therefore, 

 at C, there will be an image of A. In the same manner the rays 

 issuing from every point along A B may be traced, and will be found 

 to have each one its respective conjugate lying on C D, so the con- 

 jugate of B is at D. Hence it is at once manifest that an inverted 

 conjugate image of the object A B is formed at C D. Further, it 

 will be noticed that, although the object is straight, the image of it 

 is curved towards the lens. 



If the object A B had been curved, so that it presented a convex 

 aspect to the lens, then its conjugate image CD would have been 

 more curved ; but if A B had been slightly concave towards the lens, 

 then its conjugate would have been straight. 



As before stated, the point C has been determined by tracing 

 the refraction of two rays, 1 A F and A H, through the lens. Another 

 method is, however, often employed. 



In every lens there is a point which is called its optical centre. 

 This point is such that any ray, w T hich in its refraction through the 

 lens passes through this point, will emerge in a direction parallel to 

 its path before immergence. Now as lenses for graphic and theoreti- 

 cal purposes are often assumed to be of insensible thickness, it has 

 become the practice to draw any ray passing through the optical 

 centre of the lens a straight line. Obviously, if the lens has sensible 

 thickness the ray cannot be considered a straight line, and in the 

 microscope, where the lenses are very thick in proportion to the 

 length of their foci, this method will lead to much error. Of course, 

 in those cases where it can be taken as a straight line, it saves the 

 trouble of computing a second ray to intersect the first, as any ray 

 intersecting the straight line will determine a conjugate focal point. 



In the upper part of fig. 26 the two rays, A F and A H, are 

 traced through the lens to determine the point C, but in the lower 

 part of the figure only the ray B K is traced, and the intersection of 

 this ray by the straight line B D passing through the optical centre 

 gives the point D. 



2. An image is said to be virtual when it cannot be received on 

 a screen. Fig. 27 shows how a virtual image is formed. The 

 letters are the same as in the preceding figure, so as to show the 

 analogy between the two. The fundamental difference between 

 this figure and the last is that the object A B is placed between P, the 

 principal focus, and the lens. 



We have already seen from fig. 15 that when a radiant is placed 

 before a converging lens, and nearer to it than its principal focus, 

 the rays emerging from the lens are still divergent even after their 

 refraction through the lens ; consequently they will never intersect, 



1 In the majority of the preceding diagrams the drawing has represented the 

 facts accurately ; in this instance they are diagrammatic, the size of admissible illus- 

 trations making an accurately traced ray impossible. 



