Bearing in mind the rest of the system, the objective was then “bent” into the form given by the dotted lines, and the telescope then showed beautiful definition clear to the periphery of the field, without any visible loss in the centre.
This spurious flattening cannot be pushed far without getting into trouble for it does not cure the astigmatic difference of focus, but it is sometimes very useful. Practically curvature of field is an outstanding error that cannot be remedied in objectives required to stand high magnifying powers, except by going to the anastigmatic forms similar to those used in photography.[12]
Aside from curvature the chief residual error in objectives is imperfection of achromatism. This arises from the fact that crown and flint glasses do not disperse the various colors quite in the same ratio. The crown gives slightly disproportionate importance to the red end of the spectrum, the flint to the violet end—the so-called “irrationality of dispersion.”
Hence if a pair of lenses match up accurately for two chosen colors like those represented by the C and F lines, they will fail of mutual compensation elsewhere. Figure 60 shows the situation. Here the spectra from crown and flint glasses are brought to exactly the same extent between the C and F lines, which serve as landmarks.
Clearly if two prisms or lenses are thus adjusted to the same refractions for C and F, the light passing through the combination will still be slightly colored in virtue of the differences elsewhere in the spectrum. These residual color differences produce what is known as the “secondary spectrum.”
What this does in the case of an achromatic lens may be clearly seen from the figure; C and F having exactly the same refractions in the flint and crown, come to the same focus. For D, the yellow line of sodium, the flint lens refracts a shade the less, hence is not quite powerful enough to balance the crown, which therefore brings D to a focus a little shorter than C and F. On the other hand for A′ and G′, the flint refracts a bit more than the crown, overbalances it and brings these red and violet rays to a focus a little longer than the joint C and F focus.
Fig. 60.—Irrationality of Dispersion.
The difference for D is quite small, roughly about 1/2000 of the focal length, while the red runs long by nearly three times that amount, the violet by about four. Towards the H line the difference increases rapidly and in large telescopes the actual range of focus for the various colors amounts to several inches.