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Telescopes

LEARNING OBJECTIVES

By the end of this section, you will be able to:

• 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. Although Galileo is often credited with inventing the telescope, he actually did not. What he did was more important. 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.

Figure 1a 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.

Figure 1. (a) Galileo made telescopes with a convex objective and a concave eyepiece. These produce an upright image and are used in spyglasses. (b) Most simple telescopes have two convex lenses. The objective forms a case 1 image that is the object for the eyepiece. The eyepiece forms a case 2 final image that is magnified.

The most common two-lens telescope, like the simple microscope, uses two convex lenses and is shown in Figure 1b. The object is so far away from the telescope that it is essentially at infinity compared with the focal lengths of the lenses (d_o ≈ ∞). The first image is thus produced at d_i = f_o, as shown in the figure. To prove this, note that

${\displaystyle \frac{1}{d_{\text{i}}}=\frac{1}{f_{\text{o}}}-\frac{1}{d_{\text{o}}}=\frac{1}{f_{\text{o}}}-\frac{1}{\mathrm{\infty }}}$

Because $\frac{1}{\mathrm{\infty }}=0$, this simplifies to $\frac{1}{d_{\text{i}}}=\frac{1}{f_{\text{o}}}$, which implies that d_i = f_o, 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 1b 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, d_o′ is less than f_e, 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, $M=\frac{{\theta }^{\prime }}{\theta }$. 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

${\displaystyle M=\frac{{\theta }^{\prime }}{\theta }=-\frac{f_{\text{o}}}{f_{\text{e}}}}$

The minus sign indicates the image is inverted. To obtain the greatest angular magnification, it is best to have a long focal length objective and a short focal length eyepiece. The greater the angular magnification M, the larger an object will appear when viewed through a telescope, making more details visible. Limits to observable details are imposed by many factors, including lens quality and atmospheric disturbance.

The image in most telescopes is inverted, which is unimportant for observing the stars but a real problem for other applications, such as telescopes on ships or telescopic gun sights. If an upright image is needed, Galileo’s arrangement in Figure 1a can be used. But a more common arrangement is to use a third convex lens as an eyepiece, increasing the distance between the first two and inverting the image once again as seen in Figure 2.

Figure 2. This arrangement of three lenses in a telescope produces an upright final image. The first two lenses are far enough apart that the second lens inverts the image of the first one more time. The third lens acts as a magnifier and keeps the image upright and in a location that is easy to view.

Figure 3. A two-element telescope composed of a mirror as the objective and a lens for the eyepiece is shown. This telescope forms an image in the same manner as the two-convex-lens telescope already discussed, but it does not suffer from chromatic aberrations. Such telescopes can gather more light, since larger mirrors than lenses can be constructed.

A telescope can also be made with a concave mirror as its first element or objective, since a concave mirror acts like a convex lens as seen in Figure 3. Flat mirrors are often employed in optical instruments to make them more compact or to send light to cameras and other sensing devices. There are many advantages to using mirrors rather than lenses for telescope objectives. Mirrors can be constructed much larger than lenses and can, thus, gather large amounts of light, as needed to view distant galaxies, for example. Large and relatively flat mirrors have very long focal lengths, so that great angular magnification is possible.

Telescopes, like microscopes, can utilize a range of frequencies from the electromagnetic spectrum. Figure 4a shows the Australia Telescope Compact Array, which uses six 22-m antennas for mapping the southern skies using radio waves. Figure 4b shows the focusing of x rays on the Chandra X-ray Observatory—a satellite orbiting earth since 1999 and looking at high temperature events as exploding stars, quasars, and black holes. X rays, with much more energy and shorter wavelengths than RF and light, are mainly absorbed and not reflected when incident perpendicular to the medium. But they can be reflected when incident at small glancing angles, much like a rock will skip on a lake if thrown at a small angle. The mirrors for the Chandra consist of a long barrelled pathway and 4 pairs of mirrors to focus the rays at a point 10 meters away from the entrance. The mirrors are extremely smooth and consist of a glass ceramic base with a thin coating of metal (iridium). Four pairs of precision manufactured mirrors are exquisitely shaped and aligned so that x rays ricochet off the mirrors like bullets off a wall, focusing on a spot.

Figure 4. (a) The Australia Telescope Compact Array at Narrabri (500 km NW of Sydney). (credit: Ian Bailey) (b) The focusing of x rays on the Chandra Observatory, a satellite orbiting earth. X rays ricochet off 4 pairs of mirrors forming a barrelled pathway leading to the focus point. (credit: NASA)

A current exciting development is a collaborative effort involving 17 countries to construct a Square Kilometre Array (SKA) of telescopes capable of covering from 80 MHz to 2 GHz. The initial stage of the project is the construction of the Australian Square Kilometre Array Pathfinder in Western Australia (see Figure 5). The project will use cutting-edge technologies such as adaptive optics in which the lens or mirror is constructed from lots of carefully aligned tiny lenses and mirrors that can be manipulated using computers. A range of rapidly changing distortions can be minimized by deforming or tilting the tiny lenses and mirrors. The use of adaptive optics in vision correction is a current area of research.

Figure 5. An artist’s impression of the Australian Square Kilometre Array Pathfinder in Western Australia is displayed. (credit: SPDO, XILOSTUDIOS)

Section Summary

• Simple telescopes can be made with two lenses. They are used for viewing objects at large distances and utilize the entire range of the electromagnetic spectrum.
• The angular magnification M for a telescope is given by $M=\frac{{\theta }^{\prime }}{\theta }=-\frac{f_{\text{o}}}{f_{\text{e}}}$, where θ is the angle subtended by an object viewed by the unaided eye, θ′ is the angle subtended by a magnified image, and f_o and f_e are the focal lengths of the objective and the eyepiece.

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Devils Tower National Monument (U.S. National Park Service)

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1. Methuselah: 969 years
The oldest person in the Bible, Methuselah was Noah’s grandfather and his father walked so closely with God that God took him. Methuselah died the same year as the flood, living to 969 years of age.

2. Jared: 962 years
A descendent of Seth, Jared fathered Enoch at 162 years and lived until he was 962 years old. Genesis 5:18–20

3. Noah: 950 years
The last o the long-living antediluvian patriarchs, Noah lived for 350 years after the flood. At Noah’s birth his father said, “May he bring us relief from our work and the painful labour of farming this ground that the Lord has cursed.”

4. Adam: 930 years
The first human being, who was designed to live forever, Adam ended up only living to 930 years—not very long when compared to eternity!

5. Seth: 912 years
A brother to Cain and Abel and the only other child of Adam and Eve to be mentioned in the Bible by name, Eve named him Seth for she said, “God has granted me another son in place of Abel, whom Cain killed.” Genesis 4:25

6. Kenan: 910 years
A grandson to Seth, he fathered Mahalalel (#8) when he was 70 years old.

7. Enos: 905 years
Enos was the son of Seth (who fathered him when he was 105 years old), which makes him a grandson of Adam and Eve. Genesis 4:26; Luke 3:38

8. Mahalalel: 895 years
An ancestor of Noah and the father of Jared, Mahalalel lived until when Noah was 234 years old.

9. Lamech: 777 years 
The son of Methuselah and father to Noah, Lamech died five years before the flood. According to genealogical accounts, Adam would have still been alive for the first 56 years of Lamech’s life.

10. Enoch: 365 years

The father of Methuselah (see #1), Enoch is described in Genesis 5:24 as someone who was “walking in close fellowship with God. Then one day he disappeared, because God took him.”