CHAPTER 5

Telescopes: Windows to the Universe

CHAPTER SUMMARY

In this chapter we discuss some basic laws of optics and describe astronomical telescopes. We emphasize the three powers of a telescope: magnifying power, light-gathering power, and resolving power. This leads us to the conclusion that large reflecting telescopes are desirable. We discuss how today’s large-diameter reflecting telescopes use adaptive and active optics. We describe telescope “accessories” (instruments and detectors) and some aspects of the design of large telescopes. Finally, we discuss the importance of interferometry and of non-optical telescopes in our understanding of the universe.

LEARNING OBJECTIVES

The student who has mastered this material should be able to:

  1. Describe how refractive processes lead to image formation.
  2. Define key terms such as focal point and focal length.
  3. Describe the limitations of refracting telescopes.
  4. Understand chromatic aberration.
  5. Distinguish between magnifying power, light-gathering power, and resolving power.
  6. Be able to define field of view.
  7. Describe the advantages of a reflecting telescope.
  8. Define active optics and adaptive optics and their importance.
  9. Describe the purpose of some astronomical instruments such as photometers and spectrometers.
  10. Describe how a radio telescope works.
  11. Sketch and label the parts of a refracting and reflecting telescope.
  12. Describe how a radio wave interferometer works and its advantages.

13. Explain why space telescopes are needed and at what wavelengths they work.

CHAPTER OUTLINE

 Refraction and Image Formation

1. Light travels in a straight line as long as it remains in the same medium (i.e., the material the light is travelling through).

2. Refraction is the bending of light as it crosses the boundary (interface) between two materials in which it travels at different speeds.

3. The amount of refraction (the angle through which the light is bent) is determined by two factors: (1) the relative speeds of light in the two materials (e.g., air and glass) and (2) the angle between a light ray and the interface; the smaller the angle between a light ray and the interface, the more the light bends on passing through the interface.

4. A lens is an optical device that makes use of refraction to focus light.

5. The image is the visual counterpoint of an object, formed by refraction of light by the lens from the object.

6. The focal point (of a converging lens) is the point at which light from a very distant object converges after being refracted.

7. The focal length is the distance from the center of a lens to its focal point.

 The Refracting Telescope

1.The objective is the main light-gathering element (lens) of a refracting telescope. It is also called the primary.

2. An eyepiece (which may be a combination of lenses) added just beyond the focal point of the telescope’s objective acts as a magnifier to enlarge the image.

 Chromatic Aberration

1. Because different wavelengths are refracted by different amounts, lenses separate white light into colors (like a prism).

2. Chromatic aberration is a defect of optical systems that results in light of different colors being focused at different places. The resulting image will be fuzzy at the edges.

3. An achromatic lens (or achromat) is an optical element that has been corrected so that it is free of chromatic aberration. This is done by combining two or more lenses made of different kinds of glass.

 The Powers of a Telescope

 Angular Size and Magnifying Power

1. Angular size of an object is the angle between two lines drawn from the viewer to opposite sides of the object.

2. Magnifying power (or magnification) is the ratio of the angular size of an object when it is seen through the instrument to its angular size when seen with the naked eye.

3. The magnifying power is given byM = fobjective/feyepiece. Thus for a given telescope, using short focal length eyepieces produces more magnification.

4. Field of view is the angular width of the sky viewed by an optical instrument.

5. As magnification increases the field of view decreases.

 Light-Gathering Power

1. Light-gathering power is a measure of the amount of light collected by an optical instrument. If a telescope has more light-gathering power, fainter objects can be seen with it.

2. Light-gathering power is determined by the area of the objective. The size of the objective is usually given as a diameter. Remember that the area of a circle is proportional to the (diameter)2.

 Resolving Power

1. Diffraction is the spreading of light upon passing the edge of an object.

2. The resolution of a telescope is determined by diffraction around the objective.

3. Resolving power (or resolution) is the smallest angular separation detectable with an instrument. It is a measure of an instrument’s ability to see detail.

4. Assuming that diffraction is the only limitation, the resolving power in arcseconds is given by 2.5x105/D, where the wavelength of the light usedand the diameter of the telescope, D, are in meters. The resolving power of a human eye is about 1 arcminute (1/60 of a degree). A 30-cm (12-inch) telescope has a maximum resolving power of 1 arcsecond (1/60 of an arcminute or 1/3,600 of a degree).

5. Astronomical seeing is the blurring and twinkling of the image of an astronomical light source caused by the Earth’s atmosphere.

6. Seeing is the best possible angular resolution that can be achieved.

7. Because of atmospheric turbulence (which causes the stars to twinkle), even with the largest Earth-based telescopes the seeing is between 0.5 and 0.25 arcsecond.

8. The atmospheric effects are avoided by space telescopes. The Hubble Space Telescope has a resolving power of 0.1 arcsecond or better.

 The Reflecting Telescope

1. An inwardly curved—or concave—mirror can bring incoming light rays to a focus and is used to construct reflecting telescopes.

2. Reflecting telescopes have several advantages over refracting telescopes:

(a) There are fewer surfaces to grind and polish.

(b) Reflecting mirrors do not exhibit chromatic aberration as do lenses.

(c) Light doesn’t transmit through a mirror so imperfections in the glass are not critical.

(d) Mirrors can be supported on their backs, thus minimizing shape deformations due to gravity; lenses must be supported along their rims.

(e) It is easier to construct large diameter mirrors (compared to lenses).

  1. Because of the above advantages, all large telescopes are reflectors.

 Large Optical Telescopes

1. A Newtonian focus reflecting telescope has a plane mirror mounted along the axis of the telescope so that the mirror intercepts the light from the objective mirror and reflects it to the side.

2. A Cassegrain focus reflecting telescope has a secondary convex mirror that reflects the light back through a hole in the center of the primary mirror.

3. Prime focus is the point in a telescope where the light from the objective is focused (i.e., the focal point of the objective). In very large telescopes, observation is usually done in a cage at the prime focus.

4. The Coude design allows for large and heavy equipment to be set at the focal point, outside the main telescope tube; here light reflects off three mirrors before it exits.

5. For best viewing conditions (i.e., smallest seeing) large telescopes are located on top of mountains in dry, clear climates.

 Active and Adaptive Optics

1. Active optics is a technique of correcting any deformation of the mirror (e.g., due to motion). The mirror is constantly monitored and corrected to its optimal shape.

2. Adaptive optics is a technique that improves image quality by compensating for atmospheric turbulence and distortion.

3. To utilize active or adaptive optics the primary mirror has to be thin and deformable or constructed of segments.

 Telescope Accessories (or Instruments)

 Tools of Astronomy: Spinning a Giant Mirror

1. An ordinary camera produces images on camera film. Film is not a very sensitive detector of light.

2. A charge-coupled device (CCD) is a semiconductor chip that emits electrons when hit by light. The data collected is formed into images by a computer.

3. Photometry is the measurement of light intensity from a source, either the total intensity or the intensity at each of various wavelengths. Early photometers were like a camera’s light meter; modern photometers use a CCD for greater speed, accuracy, and light-sensitivity.

4. Spectral analysis (or spectroscopy) uses a spectrometer—an instrument that separates electromagnetic radiation according to wavelength. A spectrograph is a visual record of the spectrum taken by a spectrometer.

5. Some spectrometers use a diffraction grating—a device that uses the wave properties of EM radiation to separate the radiation into its various wavelengths.

 Radio Telescopes

1. Besides visible light, radio waves are the ones that best penetrate the atmosphere.

2. Compared to visible light, radio waves from a star have less intensity; also, their longer wavelengths lead to images of smaller resolution.

3. Bothe problems are solved by making very large radio telescopes.

4. The design of radio telescopes is similar to optical reflectors.

5. The intensity of radio waves received is represented as different colors, using computers.

 Interferometry

 Historical Note: Radio Waves from Space

1. Interferometry is a procedure that allows a number of telescopes to be used as one by taking into account the time at which individual waves from an object strike each telescope.

2. Interferometry is possible because extremely accurate atomic clocks allow for precise timing of the signals received by radio telescopes from a distant object.

3. The farther apart the telescopes, the better the resolution. The VLBA (Very Long Baseline Array) consists of 10 telescopes spaced across the United States (Virgin Islands to Hawaii). It has a resolution of a fraction of a milliarcsecond.

4. Interferometry is also employed with the newest infrared and optical telescopes as well.

 Detecting Other Electromagnetic Radiation

1. Near infrared—1,200 nm to 40,000 nm—can be detected from high, dry mountain tops such as Mauna Kea in Hawaii; water vapor is the main absorber of infrared light.

2. Far infrared—greater than 40,000 nm. This range of EM radiation is emitted by cooler objects (e.g., planets). It does not penetrate the atmosphere as well; therefore the detectors need to be airborne.

3. Infrared telescopes (such as the Spitzer Space Telescope) must be cooled so heat (IR radiation) from the surroundings does not mask the signals received from space.

  1. Ozone is the chief absorber of wavelengths shorter than about 400 nm. Observation in this range of the EM is done by space telescopes, including telescopes operating in the Ultraviolet (e.g., the GALEX telescope), in the X-ray (e.g., the Chandra telescope),and gamma-rays (e.g., the Compton and Fermi telescopes

 Tools of Astronomy

Infrared (IR): SOFIA, Spitzer, WISE, Herschel

Ultraviolet (UV): GALEX

X-ray: Chandra, XMM-Newton, NuSTAR, Fermi

Gamma-ray: Compton, INTEGRAL

The Hubble Space Telescope (HST) is mainly an optical telescope, with a 2.4-m primary mirror, but is designed to observe across the spectrum from near infrared to near ultraviolet (115–2,500 nm). Its successor is the James Webb Space Telescope, schedule to launch in 2014.

 Conclusion

 Study Guide

 Recall Questions

 Questions to Ponder

 Calculations

 Activity: Making a Telescope

 Activity: Making a Spectroscope

Expanding the Quest

TEACHING SUGGESTIONS AND CLASSROOM ACTIVITIES

In the first part of this chapter we focus on basic refracting telescopes since students can relate to them more easily, and such telescopes can be brought to class for demonstration. Even just simple lenses can be used.

During a discussion on refracting telescopes it is important to emphasize that the parallel light rays we draw indicate light coming from a single point that is at a great distance. A second set of parallel light rays come from a second point in space. As we look at the entire image, it should be obvious that all points of the lens or mirror of our telescope contribute light to all points of the image. As a result, it is possible to have an obstruction in the path of the light (as in the case of a prime focus telescope) that only reduces the amount of light received but does not block out any part of the object we observe. (This “holographic” concept may be difficult for the students to understand.)

A very simple demonstration for light refraction involves a low-power laser, a fish tank with a mirror at the bottom (for clear reflection), and a cover on top so that smoke can be trapped in the tank. The smoke makes it easier for us to see the laser beam as it travels between the air and water. (Refer students to the pencil in Figure 5-2b).

When discussing the resolution of images produced by larger telescopes, use an analogy between “normal” TVs and HDTVs. In a similar vein compare telescope CCDs to today’s ubiquitous digital cameras.

It is worthwhile to demonstrate the formation of a real image with a converging lens. If your classroom has a window and the class meets during the day, a nice image can be formed of the outside scene. Otherwise, two or three light bulbs will suffice for an object. (Most people are surprised that the image is inverted.) This demonstration leads directly to an explanation of cameras and to photography at the prime focus of a telescope. In fact, one can use a small telescope to show that an image is formed at the prime focus. Since most people have used a converging lens as a magnifier, the transition to use of a second lens as an eyepiece is an easy one.

Binoculars also make a good demonstration of the properties of an optical instrument (especially how they produce magnification and a “non-fuzzy” instrument. You can also point out the large amount of “backyard” amateur astronomy that can be done with only binoculars

In discussing light-gathering power, compare the objective of a telescope to the pupil of an eye; the pupil changes size to control the amount of light entering. To illustrate that it is the area rather than the diameter that is important, compare telescopes to pizzas. (Which has more area, two 8-inch pizzas, or one 12-inch pizza? Some pizza retailers depend upon people not understanding this idea.). Actually buy the pizzas and bring them in for the demonstration and then let the students eat them. Experience shows that demonstrations involving any type of food are remembered better and longer by students.

In every class there are some students who want advice about buying their own telescope. It is useful to stress that they should buy the largest diameter telescope that they can afford since it will have the largest light-gathering power. That should be their prime consideration. It is also important to de-emphasize the magnification specifications.

A simple single-filament incandescent lamp (sometimes called a showcase lamp) can be used to show diffraction. Cut slits in index cards, pass them out to the students, and ask the students to look through the slits at the lamp as they flex the slits open and closed. You can even look through a small opening formed between the fingers, but the cards work better.

Figure 5-9 was easy to make, and you might consider a similar project for students. A lens was used in front of a low-powered helium-neon laser to diverge the beam, and a screw was mounted a few feet in front of a SLR camera. Remove the lens from the camera so that the shadow falls directly on the film. Exposure time is not critical; use the automatic feature of the camera. Reflection of radio waves from non-shiny surfaces can be compared to the reflection of the waves in a microwave oven by the screen in the glass door.

The term adaptive optics is commonly used to describe fast changes in a telescope system to compensate for fast timescale atmospheric effects. In many cases the adaptive optics system will have a deformable mirror conjugate to the atmospheric layer and this mirror will deform to correct atmospheric distortions. Active optics is often used to refer to changes in the telescope optical system to compensate for slower changes (such as thermal changes) that may affect image quality. Systems that adjust the support and figure of the primary mirror fall into this category. Both active and adaptive optical systems are being used at present with 8-meter class telescopes.

KEY TERMS

medium / magnifying power / Cassegrain focus
refraction / field of view / prime focus
image / light-gathering power / Coudé focus
focal point / diffraction / adaptive optics
focal length / resolving power / active optics
objective lens / concave / charge-coupled device (CCD)
eyepiece / convex / photometry
dispersion / astronomical seeing / spectrometer
chromatic aberration / seeing / diffraction grating
achromatic lens / Newtonian focus / interferometry
angular size

QUESTIONS TO TEST STUDENT UNDERSTANDING

  1. Which light bends more when going through a prism, light of long wavelength or short wavelength? How does the focal length of a lens depend upon the wavelength of light?
  2. Suppose you have the following three lenses and wish to make a simple telescope for your little sister:

telescope / focal length / diameter
X / 15 cm / 5 cm
Y / 30 cm / 2 cm
Z / 20 cm / 4 cm

(a) Which lens should be used as an objective in order to produce the most light-gathering power?

(b) Which lens should be used for the objective and which for the eyepiece in order to produce the greatest magnification?

  1. What is it about a lens that determines whether it will have a short or long focal length?
  2. Since the magnification of a telescope can be changed by changing the (relatively inexpensive) eyepiece, why is there a limit to the magnification of a telescope?
  3. Suppose that your observer’s almanac suggests that you use a low magnification to view a given nebula.