116 THEORY OF THE MICROSCOPE 



It is necessary therefore to use glass with a high refractive index but 

 low dispersive power to obtain an achromatic flat image. It is only recently 

 that Messrs. Schott of Jena have succeeded in making such a glass barium 

 silicate glass which produces a greater refraction and a smaller dispersion 

 than crown glass. 



B. The eyepieces. 



An eyepiece is a system of lenses so arranged that the real image produced 

 by the objective in the tube is magnified and trans- 

 mitted to the eye of the observer. 



In practice it is found expedient to form the eyepiece 

 of two plano-convex lenses separated by an interval ; 

 the lower lens is called the field-lens, for it increases 

 the field of view of the instrument, the upper lens 

 is called the eye-lens. 



The eyepiece most commonly used is that known 



FIG. 110. Theory of Huy- ,, __- 7 . . J 



genian eyepiece. as the Huygenian eyepiece. 



(To render the figure less In its simplest form this eyepiece consists of two 



otS?\vi&e\ppear, theprin- plano-convex lenses a field-lens F, and an eye-lens 



cipal plane is taken as on E Tne f oca i i en gth of the former /, is three times 



the flat side of the lens.) 0,11, Prm a J r 11 



that of the latter / 2 . The curved surface of each lens 



faces the incident light, and the lenses are separated by an interval d which 

 is twice the focal length of the eye-lens. 



Thus f l =3/,, and d = - 2/,. 



Let ba (fig. 110) represent the aplanatic image of the object formed by the objec- 

 tive. The field- lens of the eyepiece is placed below it, indeed half its focal length 

 below it. Consequently the image ba is not actually formed, but the converging 

 pencils proceeding towards the separate points of the image ba are made by the 

 field-lens to converge towards the separate points of the image b'a'. Now since 

 the cone of light that corresponds to any point of the image ba meets only an 

 exceedingly small portion of the field-lens, we may neglect the aberrations which 

 occur within each of these cones. Therefore we may regard each point of the 

 image b'a' as being fairly distinct ; but it is necessary to consider in what way 

 the spherical aberration of the field-lens will affect their relative positions. Now the 

 field-lens may be regarded as consisting of several annular zones, the refracting power 

 of each zone increasing with its distance from the centre. The axial ray of the 

 peripheral pencil aa' will consequently undergo a greater deviation than that of the 

 intermediate pencil such as yc. The consequence of this will be that the image 

 b'a' will be 



1. Curved, because the refracting power of the peripheral portion of the field- lens 

 being greater than the more central portion, the focus a' of the peripheral pencil 

 will be nearer the lens than the focus c of the intermediate pencil. 



2. Distorted, for the peripheral parts of the image ca' will be smaller than the 

 more central part b'c, i.e. the distortion is barrel-shaped (p. 109). 



3. Smaller than the image ba. 



In the majority of text- books the Huygenian eyepiece is also proved to be 

 achromatic. But the proof is only applicable for incident parallel rays. The eye- 

 piece does not give a strictly achromatic image of the objective's image, so that 

 the proof is not worth considering. It has already been said that the apochromatic 

 objective forms larger blue images than red. The compensating eyepiece having 

 the eye-lens of a flint and crown glass combination forms larger red images than 

 blue, and consequently the final image is completely achromatic. 



It will be obvious from what has been said that there are so many errors 

 to correct that it would appear well nigh impossible to correct them all. So 

 would it be were it necessary to form a point image on the retina of each 

 point of the object ; fortunately the structure of the retina obviates this 

 necessity. The smallest visual area of the retina is a retinal cone. In the 



