The Keplerian Telescope

The Keplerian Telescope. An improvement on Galileo's telescope was made in 1611 by Johannes Kepler, a German astronomer and former pupil of Tycho, who suggested that the converging rays from the objective be allowed to come to a focus, and that the resultant image be magnified with a convex lens.

Fig. 3 shows the
advantage of this new arrangement. The rays, upon emergence from the eye lens, are now converging; hence more of them and a wider
field of view can be taken in by the eye. Projected backward through the eye lens, the rays appear to proceed from B'A', where a virtual image, inverted and enlarged, is formed. As before, the amount of magnification is in the ratio of angle c' to angle c.

Fig. 3. Image formation in the Keplerian (inverting) telescope.

Considerably higher magnification can be had with this inverting telescope. But with increasing magnification, the inherent defects of a lens, notably chromatic and spherical aberration (Figs. 4 and 5) were likewise increased. The aberrations could be diminished to a considerable extent by lengthening the focus of the objective lens.

Consequently, in efforts to reduce these aberrations, enormous proportions were reached, instruments of 130 and 150 feet in length being constructed. Lens diameters up to six inches and more were attained. Non-spherical surfaces were also attempted in an endeavor to overcome spherical aberration. With these extremely long telescopes, working fields of only two or three minutes of arc must have been the rule. For comparison, the angular diameter of the planet Jupiter (at closest opposition) is almost one minute of arc, so the trials and patience of these 17th-century astronomers in aiming their exceedingly long instruments can be appreciated.

Magnification is a secondary consideration of the telescope; its chief function is to collect light. The eye alone gathers a limited amount of light, hence the luminosity of an object determines its visibility; also, the unaided eye can resolve only a limited amount of detail. An objective lens of the same diameter as the pupil of the eye would not improve vision, regardless of the amount of

Fig. 4. Chromatic aberration in a convex lens. The amount of "bending" undergone by a ray of light depends on the refractive index of the glass. As the index is different for different wave lengths, and greatest for the shortest waves, a refracted ray of white light is dispersed into its component colors, blue being brought to a focus nearer to the lens than yellow or red light.

magnification employed, except that through this enlargement the detail in an object would be made more apparent. A 1-inch objective lens, assuming it to be about 3½ times the diameter of the eye pupil (about seven millimeters at night), collects about 13 times as much light, and correspondingly fainter objects become visible.

The amount of detail seen is also increased, due to the greater aperture. So it is evident that the early observers needed larger objectives for greater light-gathering and resolving power. But since spherical aberration increases with the square of the aperture, the only way in which it could be kept under control
was to lengthen the focus, but there was a practical limit to what lengths could be handled. Moreover, a larger field of view was

Fig. 5. Spherical aberration in a convex lens. Rays striking the different zones of a convex lens having spherical surfaces (or of a concave spherical mirror) are not brought to the same focus, edge-zone rays intersecting the axis at a point nearer to the lens (or mirror) than central-zone rays

greatly desired, and this could accrue only with the use of shorter focal lengths. While spherical aberration could be pretty well eliminated by the use of two suitably curved lenses of the same kind of glass, there still remained chromatic aberration to be contended with.

In the hope of combining lenses of different glasses in such a way as to overcome chromatic aberration, Sir Isaac Newton attempted to determine if refraction and dispersion3 were the same in all optical media. Although his experiment was inconclusive, from it Newton assumed that refraction and dispersion were proportional to each other, and he decided that nothing could be done to improve the refractor. He therefore directed his energies to the formation of images from concave reflecting surfaces, which are perfectly achromatic.

Gregorian Telescope