Astronomy Assignment – Electromagnetic Radiation and Telescopes

Reading: The student is responsible for some, but not all, of the material in Chapters 3, 4, and 5.

Objectives/HW

The student will be able to:		HW:
1	Define, illustrate, and apply the basic wave concepts of frequency, wavelength, and speed and relate these to source and medium.	1
2	Solve mathematical problems involving speed, frequency, and wavelength.	2 – 4
3	Describe and illustrate the nature of electromagnetic radiation.	5
4	State the six major regions of the electromagnetic spectrum in order of frequency and/or wavelength.	6 – 8
5	State the colors of the visible spectrum in order of frequency and/or wavelength.
6	Define, illustrate, and apply the concepts of reflection, refraction, dispersion, diffraction, interference, opacity and transparency.	9 – 10
7	Explain, illustrate, and apply the basic concepts of blackbody radiation.	11 – 12
8	Solve mathematical problems using Wein’s law.	13 – 15
9	Explain, illustrate, and apply the concept of the Doppler effect and the astronomical terms of redshift and blueshift.	16 – 17
10	State and apply Kirchoff’s Laws of continuous, emission, and absorption spectra and describe the components and operation of a spectroscope.	18 – 21
11	Explain how spectral lines and the width and intensity of those lines are related to properties of atoms and or molecules.	22 – 25
12	Describe and illustrate the two main types of optical telescopes – refracting and reflecting and contrast in terms of resolution, light gathering, and aberrations.	26 – 32
13	Describe how the Earth’s atmosphere affects astronomical observations and current efforts to improve ground-based astronomy.
14	Compare and contrast telescopes that create images using nonvisible radiation.
15	Solve mathematical problems relating magnification to focal lengths of objective and ocular.	33 – 34
16	Solve mathematical problems involving the diffraction limit and relating angular resolution to wavelength and diameter.	35 – 38
15	Solve mathematical problems involving light gathering capacities.	39 – 42

Homework Problems and Questions

1. For any given type of wave moving through a certain medium what happens to the speed and to the wavelength if the frequency of the wave is increased?

2. A sound wave moving through water has a frequency of 256 Hz and a wavelength of 5.77 m. (a) What is the speed of sound through the water. (b) What will be the wavelength of this same sound if it goes from the water into the air (where the speed of sound is 343 m/s)?

3. Determine the wavelength of the following radio stations:
(a) AM 990 kHz and (b) FM 93.1 MHz.

4. Determine the frequency and color of light with each of the following wavelengths: (a) 500 nm, (b) 700 nm, (c) 590 nm. (See Figure 3.9, p. 70)

5. What we all call “light” is simply the “stuff” we see with our eyes. To a scientist however, light is just a certain type of electromagnetic radiation. (a) What does visible light have in common with other types of electromagnetic radiation? (b) What makes visible light different from other types of electromagnetic radiation?

6. Beside each astronomical picture in your book is a key labeled R I V U X G. (a) What does the key tell about each picture? (b) What do the letters stand for? (c) Why are the letters arranged in this order?

7. The Chandra X-Ray Observatory orbits Earth and takes images of the cosmos using wavelengths in the range 0.12nm to 12 nm. In spite of the observatory's name, the lowest frequency it images might be considered to be ultraviolet - what frequency and wavelength is this?

8. The James Webb Space Telescope is designed to be sensitive to radiation with frequencies from 10.5 to 500 THz. Determine the range of wavelengths and the two types of radiation measureable by this telescope.

9. Reflection, refraction, dispersion, diffraction and interference are phenomena exhibited by all types of waves. (a) When looking at a rainbow, the Sun is always behind you and the colors are coming from an arc of raindrops in front of you – which of the listed phenomena are involved? Explain. (b) Multi-path distortion occurs when listening to a radio station and the antenna is detecting waves that have followed two different paths from the station to you – which phenomena are involved? Explain.

10. Astronomers say that Earth’s atmosphere has a radio window at wavelengths of about 1 cm to 10 m. (a) Explain what the radio window is by using words like opaque/opacity and/or transparent/transparency. (b) There is also a range of wavelengths called the optical window – what two types of radiation can “come through this window”? (see Fig. 3.9, p. 70)

11. (a) Explain what is meant by blackbody radiation. (b) According to Wien’s law what happens to the emitted radiation of an object as its temperature is increased? (c) According to Stefan’s law what happens to the emitted radiation of an object as its temperature is increased?

12. Look at the photograph of the constellation Orion on page 446, Figure 17.8. The two brightest stars are Betelgeuse (upper left) and Rigel (lower right). Judging by the appearance in the photograph, which do you believe has a higher temperature and how can you tell?

13. Use Wein’s law to determine the temperature of a certain star based on the fact that it’s spectrum has a peak intensity at about 490 nm.

14. Stars can vary a lot in temperature. Astronomers categorize stars into different types based partly on this fact. Determine the frequency and type of radiation at which the spectra of each of these types of stars would have a peak intensity: (a) a type O star with temperature 30,000 K and (b) a type M star with temperature 3000 K.

15. Normal human body temperature is about 37 °C. Due to this inherent temperature the human body gives off radiation. Determine the peak wavelength and frequency of this radiation. What type of radiation is it?

16. (a) What is the Doppler effect? (b) What happens to wavelength when radiation undergoes a redshift? (c) What causes a redshift in radiation?

17. The speed of a baseball pitch is measured by a radar gun that is located behind home plate. The radar signal is reflected from the baseball as it moves toward home plate. (a) What happens to the speed, wavelength, and frequency of the reflected radar signal? (b) Would this be considered a redshift or a blueshift? Explain.

18. (a) Why is spectroscopy such an important “tool” for astronomers? (b) The key component in a spectroscope is either a prism or a diffraction grating. What is the purpose of either of these? (i.e. What does it do?)

19. How is the emission spectrum produced by a certain element related to the absorption spectrum produced by the same element? Explain why this relationship exists.

20. When light passes through a nebula (a cloud of low density gasses) it may or may not be absorbed by the atoms in nebula. What has to happen for the light to be absorbed? What has to happen for it to pass through without being absorbed?

21. The Sun’s spectrum is a combination of a continuous spectrum (a blackbody curve) and an absorption spectrum that shows up as dim gaps in the otherwise continuous spectrum. (a) What part of the Sun produces the continuous spectrum? Use Kirchoff’s Laws to explain this. (b) What part of the Sun causes the absorption dark lines? Use Kirchoff’s Laws to explain this.

22. The intensity of the hydrogen alpha (Hα) line in the spectrum of the Sun is not very great even though the Sun is mainly made out of hydrogen. What would prevent atoms of hydrogen from absorbing or emitting this particular line?

23. Molecular gas can emit or absorb radiation due to energy changes other than electron transitions. What are two types of changes in energy state that a molecule can undergo that a solitary atom (monatomic gas) cannot?

24. Suppose two stars have absorption lines at the same wavelength and intensity but star B’s lines are broader (wider) than star A’s. (a) What properties would the two stars share as evidenced by having the same lines? (b) What difference(s) in star B could possibly explain the greater width of its lines?

25. As the temperature of a gas is increased the emission spectra that it produces will change. Describe at least two changes that will occur in the bright lines as the temperature increases. And explain why each change occurs.

26. Why do astronomers desire larger and larger telescopes? In what ways do larger diameter scopes improve the ability of astronomers to analyze distant objects?

27. What is the difference between refracting telescopes and reflecting telescopes? Describe three advantages of reflectors over refractors.

28. Aberrations occur in all telescopes to some extent. (a) The term “aberration” (in connection with telescopes) indicates inability of the optics to correctly do what? (b) Which type of aberration is caused by an incorrect shape of the lens or mirror? (c) Which type of aberration can cause false colors in the image produced by a telescope?

29. Radio telescopes are often very large – for example China’s FAST telescope with reflector of diameter 1650 feet (0.31 miles!) Describe two reasons why it is desirable to have very large telescopes when observing in the radio portion of the electromagnetic spectrum.

30. The Hubble Space Telescope (HST) is one of the best telescopes ever (so far). (a) The main reason to put HST in space was to get it above the Earth’s atmosphere. What problems does the atmosphere cause for telescopes on the ground? (b) What are some disadvantages to having HST in orbit?

31. Since the late 1990’s, astronomers have relied more and more on electronic images made with CCD detectors (digital chips) that can be stored, viewed, and processed on a computer. This has almost completely replaced the older technology of film cameras. (a) Discuss at least two advantages of digital images over film images. (b) Discuss disadvantages.

32. Because of the advancement of adaptive optics it is no longer necessary to put a telescope into orbit to avoid atmospheric blurring. (a) Describe how adaptive optics compensate for atmospheric blurring. (b) What are other reasons that it still may be desirable to place telescopes in space?

33. An eyepiece with focal length 40 mm is used in a telescope that has a primary mirror with focal length 1400 mm. (a) What is the magnification? (b) If the same eyepiece is used in a refractor with focal length 600 mm what will be the magnification?

34. In order to achieve a magnification of 120 power using a telescope that has an objective with focal length 2000 mm, you would need an eyepiece with what focal length?

35. A certain “binary star” actually consists of two stars that are separated by 0.5 arc seconds as seen from Earth. In order to resolve this double star (i.e. be able to see it as two separate objects) you would need to observe it through a telescope with at least what minimum diameter, in inches? (Assume an operating wavelength of 600 nm – visible light)

36. A certain space-based telescope can achieve (diffraction-limited) angular resolution of 0.05″ for red light of wavelength 700 nm. What would this telescope’s resolution be (a) in the infrared, at 3.5 μm, and (b) in the ultraviolet, at 140 nm?

37. Estimate the angular resolutions of (a) a radio interferometer with a 5000 km baseline, operating at a frequency of 5 GHz and (b) an infrared interferometer with a baseline of 50 m operating at a wavelength of 1 μm.

38. During opposition, the planet Saturn is at a distance of about 1300 Gm from the Earth. At that distance a telescope can resolve only features of a certain size. Features of Saturn smaller than this size remain “invisible”. Determine this size for each telescope given its resolving power: (a) the Hale telescope (1″), (b) HST (0.05″), and (c) a radio interferometer (0.001″).

39. The school’s telescope is a Celestron C-8, which has a primary mirror with a diameter of 8.0 inches. (1 inch = 2.54 cm) The light entering the telescope has wavelength approximately equal to the center of the visible spectrum – about 600 nm. (a) By what factor does this telescope improve your eye’s light gathering capacity if your pupil has a diameter of 5 mm? (b) Determine the theoretical diffraction limit on this telescope’s angular resolution.

40. Based on collecting areas, how much more sensitive would you expect the 300-m Arecibo (Figure 5.24) to be, compared with the 105-m Green Bank instrument (Figure 5.23)?

41. A 2 m telescope can collect a given amount of light in 1 hour. Under the same observing conditions, how much time would be required for a 6 m telescope to collect an equal amount of light? How about a 12 m telescope? (Note: When astronomers refer to the “size” of a telescope, such as 2 m, it is the diameter of the telescope’s objective lens or mirror.)

42. The photographic equipment on a telescope is replaced by a CCD. If the photographic plate records 5% of the light reaching it, while the CCD records 75%, how much time will the new system take to collect as much light as the old detector recorded in a 1-hour exposure?

Selected Answers

2. a. 1480 m/s

b. 1.34 m

3. a. 303 m

b. 3.22 m

4. a. 6.0 x 10¹⁴ Hz, g

b. 4.3 x 10¹⁴ Hz, r

c. 5.1 x 10¹⁴ Hz, y

5. a.

6. a.

7. 2.5 x 10¹⁶ Hz, 12 nm

8. 0.60 μm, 29 μm; visible (red and orange) and infrared

9. a.

10. a.

11. a.

12.

13. 5900 K

14. a. 3.1 x 10¹⁵ Hz, UV

b. 3.1 x 10¹⁴ Hz, IR

15. 9.4 x 10^-6 m

3.2 x 10¹³ Hz, IR

16. a.

17. a.

18. a.

19.

20.

21. a.

22.

23.

24. a.

25.

26.

27.

28. a.

29.

30. a.

31. a.

32. a.

33. a. 35 times

b. 15 times

34. 17 mm

35. 12 inches (0.30 m)

36. a. 0.25″

b. 0.01″

37. a. 0.003″

b. 0.005″

38. a. 6000 km

b. 300 km

c. 6 km

39. a. 1650 times

b. 0.74″

40. 8.2 times as sensitive

41. 6.67 minutes (6 m)

1.67 minutes (12 m)

42. 4 minutes