Chapter 11 Vision and Optical Instruments
11.5 Telescopes
Summary
- Outline the invention of a telescope.
- Describe the working of a telescope.
Telescopes are meant for viewing distant objects, producing an image that is larger than the image that can be seen with the unaided eye. Telescopes gather far more light than the eye, allowing dim objects to be observed with greater magnification and better resolution. The first patent for a telescope was issued in 1608 to Hans Lippershey of the Netherlands. https://en.wikipedia.org/wiki/History_of_the_telescope. Galileo is often credited with inventing the telescope in 1609, because of the important work he did with it. He constructed several early telescopes, was the first to study the heavens with them, and made monumental discoveries using them. Among these are the moons of Jupiter, the craters and mountains on the Moon, the details of sunspots, and the fact that the Milky Way is composed of vast numbers of individual stars. This is one the greatest paradigm shifts in the history of science. If you want to read more about this, here is a link to an excellent article https://phys.org/news/2009-10-paradigm-shift-galileo-spy-glass.html.
Figure 1(a) shows a telescope made of two lenses, the convex objective and the concave eyepiece, the same construction used by Galileo. Such an arrangement produces an upright image and is used in spyglasses and opera glasses.
The most common two-lens telescope, like the simple microscope, uses two convex lenses and is shown in Figure 1(b). The object is so far away from the telescope that it is essentially at infinity compared with the focal lengths of the lenses (do ≈ ∞). The first image is thus produced at di = fo , as shown in the figure. To prove this, note that
Because 1/∞ = 0 this simplifies to
which implies that di = fo , as claimed. It is true that for any distant object and any lens or mirror, the image is at the focal length.
The first image formed by a telescope objective as seen in Figure 1(b) will not be large compared with what you might see by looking at the object directly. For example, the spot formed by sunlight focused on a piece of paper by a magnifying glass is the image of the Sun, and it is small. The telescope eyepiece (like the microscope eyepiece) magnifies this first image. The distance between the eyepiece and the objective lens is made slightly less than the sum of their focal lengths so that the first image is closer to the eyepiece than its focal length. That is, do‘ is less than fe, and so the eyepiece forms a case 2 image that is large and to the left for easy viewing. If the angle subtended by an object as viewed by the unaided eye is θ, and the angle subtended by the telescope image is θ’, then the angular magnification M is defined to be their ratio. That is, M =θ’. It can be shown that the angular magnification of a telescope is related to the focal lengths of the objective and eyepiece; and is given by
The minus sign indicates the