Astronomy Assignment – Electromagnetic Radiation and Telescopes
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The student will be able to: |
HW: |
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1 |
Define, illustrate, and apply the basic wave concepts of frequency, wavelength, and speed and relate these to source and medium. |
1 |
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2 |
Solve mathematical problems involving speed, frequency, and wavelength. |
2 – 4 |
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3 |
Describe and illustrate the nature of electromagnetic radiation. |
5 |
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4 |
State the six major regions of the electromagnetic spectrum in order of frequency and/or wavelength. |
6 – 8 |
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5 |
State the colors of the visible spectrum in order of frequency and/or wavelength. |
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6 |
Define, illustrate, and apply the concepts of diffraction, interference, opacity and transparency. |
9 – 10 |
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7 |
Explain, illustrate, and apply the basic concepts of blackbody radiation. |
11 – 12 |
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8 |
Solve mathematical problems using Wein’s law. |
13 – 15 |
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9 |
Explain, illustrate, and apply the concept of the Doppler effect and the astronomical terms of redshift and blueshift. |
16 – 17 |
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10 |
Describe the characteristics of continuous, emission, and absorption spectra and the conditions under which each is produced. |
Chpt 4 R&D 1 – 4, 11 – 20 |
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11 |
Explain how spectral lines and the width and intensity of those lines are related to properties of atoms and or molecules. |
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12 |
Describe and illustrate the two main types of optical telescopes – refracting and reflecting and contrast in terms of resolution, light gathering, and aberrations. |
Chpt 5 R&D 1, 2, 4 – 8, 10 – 13, 15, 16, 19, 20 |
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13 |
Describe how the Earth’s atmosphere affects astronomical observations and current efforts to improve ground-based astronomy. |
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14 |
Compare and contrast telescopes that create images using nonvisible radiation. |
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15 |
Solve mathematical problems involving light gathering capacities. |
18 – 20 |
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16 |
Solve mathematical problems relating angular resolution to wavelength and diameter. |
21 – 25 |
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17 |
Solve mathematical problems relating magnification to focal lengths of objective and ocular. |
26 – 27 |
Chapter 3
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. 71)
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. A certain telescope was placed in orbit to image the sky using wavelengths of around 25 nm. Determine the frequency and type of radiation that this telescope used.
8. A different telescope was designed to be sensitive to radiation with frequency of around 6000 GHz. Determine the wavelength and type of radiation used by this telescope.
9. Diffraction and interference are phenomena exhibited by all types of waves. Explain what each of these words means and give an example of each.
10. (a) Define the word opacity. (b) The Earth’s atmosphere is opaque to what types of radiation? (c) The Earth’s atmosphere is transparent to what range(s) of wavelengths?
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 445, 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.
p. 104: Review and Discussion 1 – 4, 11 – 20
p. 139: Review and Discussion 1, 2, 4 – 8, 10 – 13, 15, 16, 19, 20
18. Based on collecting areas, how much more
sensitive would you expect the 300-m
19. 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.)
20. 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?
21. 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)
22. 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 mm, and (b) in the ultraviolet, at 140 nm?
23. 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 mm.
24. 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”).
25. 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.
26. 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?
27. 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?
Selected Answers
HW handout
1.
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.
b.
6. a.
b.
c.
7. 1.2 x 1016 Hz, UV
8. 50 mm, IR
9. diffraction = ?
interference = ?
10. a.
b.
c.
11. a.
b.
c.
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.
b.
c.
17. a.
b.
Review and Discussion
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20.
Review and Discussion
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HW handout
18. 8.2 times as sensitive
19. 6.67 minutes (6 m)
1.67 minutes (12 m)
20. 4 minutes
21. 12 inches (0.30 m)
22. a. 0.25”
b. 0.01”
23. a. 0.003”
b. 0.005”
24. a. 6000 km
b. 300 km
c. 6 km
25. a. 1650 times
b. 0.74”
26. a. 35 times
b. 15 times
27. 17 mm