The three limits of behavior can also be described using the concept of a field-stop. In the low magnification limit the field-stop of the system is the objective lens whereas in the high magnification limit the field-stop is the pupil of the eye. If the eye is allowed to move, the field stop is the edge of the eyepiece. I have taken two series of photographs that illustrate the different behaviors. To do that, I needed to make two very different telescopes. The first is a low magnification telescope shown here. The telescope is constructed very simply from a cardboard mailing tube, lined with flock paper. The objective has a focal length of 500 mm and the eyepiece is a negative lens with a focal length of -170 mm. The magnification is therefore approximately 3. Both lenses have diameters of 50 mm. This is probably larger than was available in good quality in 1609, but I wanted to make sure that the exit pupil was large. In fact, the exit pupil is 17 mm in diameter, much larger than either a daytime adapted eye, about 3 mm, or a night-adapted eye, about 6 mm.
My second telescope is a much more conventional Galilean replica. The objective has a focal length of 1000mm. Its diameter is 25.4 mm, but by the time it was mounted this was masked to about 23 mm. I used two eyepieces, with focal lengths of -50 mm and -30 mm, giving magnifications of 20 and 33 respectively. The eyepiece diameters were also 25.4 mm. The exit pupils with the two eyepieces were 1.15 mm and 0.7 mm, which are both much smaller than a dark adapted eye. I took a second series of photographs using this telescope. The planisphere still subtends an angle of 0.5 degrees. I used the 20x magnification eyepiece so that the exit pupil of the telescope is 1.15 mm in diameter. This time, the iris of the camera lens is the field stop, and I took the photographs using different apertures for the 50 mm lens on the camera. The telescope was not adjusted at all during the series.
A more serious comment is that the last photograph gives you some idea of what you can see by moving your eye around behind the eyepiece. Clearly the image of the whole planisphere, and hence of the whole Moon at night, is getting out of the telescope. A related point is that the telescope can also be used to project an image of the Sun, and the image of the entire disk of the Sun is projected. In this series of photographs I didn't reach the final limit, that the eyepiece of the telescope acts as the field stop. If the camera lens could have been opened much more, or if I had moved the camera slightly to one side, I would have seen the slightly rough edge of the mounting of the eyepiece limiting the view. |