How Large a Diagonal part 3
The black spot is relatively larger for higher-power eyepieces,
and for an eyepiece of 14" focal length, which takes in a very much smaller field, the unserviceable part of the mirror expands to a diameter only Vs" less than that of the gray zone.
Thus, the mirror maker now realizes that he need not be unduly alarmed about surface defects of any nature in a central area of the mirror of diameter about equal to the width of his diagonal. This also explains why there is no loss in perforating the primary when a
Cassegrainian telescope is made.
As the reader may demonstrate to his own satisfaction, these findings regarding the proportions of the centrally obstructed areas apply to any size mirror, of any focal ratio, for linear fields of view of similar diameter (about 1"). Small variations in the width of the gray zone occur as a result of relative differences in the distance of the diagonal inside of focus.
Thus it is seen that the larger the diagonal, the less light there is in the image. More serious, though, is the diffraction that is introduced. This becomes conspicuous when the area of the obstruction exceeds six per cent of that of the mirror. (See the discussion on diffraction in Chapter XIII.) For these reasons, it is important that the size of the diagonal be kept at a minimum compatible with the needs of the observer. The area of the mirror obstructed by a diagonal measuring 1.7" x 2.4" is, if rectangular, 10.3 per cent, and if elliptical, eight per cent of the total. The low-power eyepiece for which this size diagonal is designed is used almost exclusively as a "finder"; when the object sought has been located and centered in the field, the observer invariably switches to an eyepiece of higher power. It is not logical, therefore, to saddle the telescope with a lot of light obstruction and harmful diffraction from a needlessly large diagonal.
The larger diagonal may be justified only in the case of a mirror of low focal ratio, designed for use with low power, where a wide field of view is desired for such observations as the exploration of star fields, comet seeking, and so on. Even there
(except for the specific case of variable star work, when the tube, too, should not cut off any part of the field) it is most likely that use of a diagonal of, say, l½" in width, of elliptical shape, and obstructing but six per cent of the mirror's area, would prove far more advantageous than the size prescribed by geometry.
For our f/8 mirror, a minimum practical size may be arrived at from the fact that its field of reasonably good definition is about 30 minutes of arc in width, about the size of the moon. The linear size of the moon's image is found in this way: the tangent of 30' is 0.0087, which, multiplied by 48 (the focal length of the mirror), gives 0.4176" or about 2/5" at the focus. Substituting this value for the width of VV, Fig. 47, the size of the diagonal derived from the formula is then, in even fractions, 1 3/16" x 1 5/8". Its area of obstruction, if rectangular, is five per cent, and if elliptical, four per cent of that of the mirror. The amount of light obstructed by it is at a near minimum, and diffraction is reduced to the vanishing point.
The effect on the field of view of this small diagonal in actual observations is illustrated in Fig. 49, where the fully illuminated part of the field, occupied in a and b by the picture of the moon's disk, is shown as it would appear through eyepieces of 11/2", 1", and 14." focal lengths, each having an apparent field of 36°. In the first instance, there is a gradual and probably unnoticeable falling off of illumination approaching the edge of the field, so that, for a single star at the extreme edge, the equivalent of slightly less than a 51/4-inch mirror is employed, which is hardly too bad.
The losses in the second instance are of insignificant quantity, while in the third instance, the image of the moon (or fully illuminated field, outlined by the dotted circle) is too large to be fitted into the field of view of that eyepiece. If one is situated in a locality where the seeing is generally good, so that high magnifications can be consistently used, a still smaller diagonal might reasonably be chosen, but there appears to be little reason for making it larger.
Preliminary Preparations
|
|
