1.3. Optical system of a telescope

FIGURE 5: Image formed by a telescope mirror objective, as seen without the eyepiece (flat is omitted for simplicity). Wavefronts emitted from distant object of height h become practically flat over the aperture of a telescope, here a concave mirror M. The mirror changes the shape of the incoming flat wavefront section (W) into spherical (W') by delaying reflection of the points in phase belonging to the wavefront's inner area. Point of convergence (c) - or focal point - is at the center of curvature R of the wavefront. Thus, with the stop at mirror surface and exit pupil plane at mirror vertex, the mirror focal length equals the radius of the wavefront in the pupil.  The top point of distant object h, at an angle α from the optical axis, is imaged into (reversed) top of the image h' by off-axis wavefront Wa, originating at the object's top point. If observed directly, from the least distance of distinct vision v (approx. 25cm, or 10 inches) most of the light from the object image h' misses the eye pupil (more so for the points farther off-axis, with no light from the image's reversed top reaching the eye); also, magnification is limited to ƒ/v, ƒ being the objective's focal length. The apparent image angle β determines objective magnification as Mo=tanβ/tanα.

FIGURE 6: Image formed by a telescope lens objective, as seen through the eyepiece. Since light is slowed down in glass, the in-phase points of the incident axial wavefront W are retarded the most in the center of the lens objective L (for simplicity, both objective and eyepiece are shown as a single lens), and the least at its edges. Properly made lens objective will re-shape flat incident wavefront W into spherical (W') after exiting the lens. That is a goal for off-axis point wavefronts (Wa) as well, although some form of deviation due to tilt-created asymmetry is usually present. In terms of rays, change in direction of straight lines orthogonal to the wavefront (rays), resulting from its new shape, is called refraction. The lens objective focal length ƒO is the distance between its second principal point P2 and the focal point F. The eyepiece (EP), placed at a distance of its focal length ƒE from the object image h' formed by the objective, converts diverging spherical wavefront into flat, for which the eye has preference. It also increases the apparent incidence angle (α vs. ε), making the object imaged at the retina (E) appear larger by a factor ~ƒO/ƒE. Use of an eyepiece allows for far more light from the object's image (all of it, if properly designed) to reach the eye, much higher magnifications, and much wider fields compared to observing image formed by the objective with eye alone.

FIGURE 7: Geometry of image formation by lens (A) and mirror (B) objective. Incident ray parallel to the optical axis (2) is directed, after reflection or refraction, to the focal point F, located at its intersection with the optical axis. It determines the focal length ƒ. Incident ray coming from the same object point through the front focus F' or F (3) refracts or reflects parallel to the optical axis; its intersection with ray (2) determines the image point location. Alternatively, it is also determined by the point of intersection with the incident ray arriving at the center of the objective (1, termed chief ray). As object distance increases, incident rays coming through the front focus and center of the objective (3 and 1, respectively) merge closer, practically merging together for very distant objects. At that point, image magnification, given as image-to-object-distance ratio, approaches zero - with the field angle α reduced to a very small, but finite quantity - and the image practically forms at the focal point location.