Solutions for Assignment #5 (Chapter 6 in the 4th edition of Bennett et al.)


Read Chapter 6

1.) What is the function of a lens or a curved mirror in a telescope?
Answer: Both change the angle of the incoming light rays (example, the lens bends the light rays) so that the rays of light will focus.

2.) How are telescope observations better than "naked eye" observations?
a.) telescopes can collect more light than a human eye can
b.) telescopes can have better angular resolution than a human eye
c.) both of the above
d.) none of the above
Answer: c

3.)
a.) In order to see the features on a planet clearly, do you want your telescope's diffraction limit to be smaller than the angular separation between the features on the planet, or do you want your telescope's diffraction limit to be larger than the angular separation between features on the planet
Answer: You want the telescope's diffraction limit to be smaller than the angular separation between the features on the planet.
b.) Explain why
Answer: The diffraction limit is the smallest angular separation that you can see with your telescope. If the features on the planet are spaced at even smaller angles than the diffraction limit, then your telescope will blur their light together and you won't be able to see the features clearly.

4.) Compare a 5 meter telescope with a 10 meter telescope:
a.) Which has the better diffraction limit and by what factor is it better than the diffraction limit
of the other telescope? (The wavelength of the light to be observed is 656 nm, but it is possible for
you to do this problem without knowing the wavelength.)
b.) Which has the larger light collecting area and by what factor?
Answer: The 10 meter telescope has a better diffraction limit. It is half as large as that of the 5 meter telescope.
b.) Which has the better light collecting area and by what factor?
Answer: The 10 meter telescope has 4 times as much light collecting area as the 5 meter telescope.

5.) Briefly describe the advantages of putting telescopes in space.
Answer: Atmospheric absorption: Some wavelengths of light are absorbed by the Earth's atmosphere.
So, for those wavelengths, the only practical way to detect the light is to have a telescope in space
(i.e. above the Earth's atmosphere). Atmospheric turbulence: Regions where the Earth's atmosphere
varies in temperature or density act like lenses. They alter the light's path and thus distort the image.
Unfortunately, the atmosphere moves turbulently, which means that these "lenses" are always on the
move, thus constantly shifting the light's path in different ways. If the telescope is on the ground, the
ever-changing image will be hard to accurately record, but if the telescope is in space, atmospheric
turbulence will not be a problem. Less importantly: Light pollution: Telescopes on Earth see some
of the photons made in streetlights, carlights, etc.. These photons pollute the observations. By
putting telescopes in space, we avoid much of this problem. Less important: Infrared telescopes
are sensitive to the photons made by the Earth's blackbody radiation. So, putting infrared telescopes
in space avoids this problem.

6.) Which one of the following could be a true statement (taken from textbook):
a.) The image was blurry because the photographic film was not placed at the focal plane
b.) Thanks to adaptive optics, the telescope on Mount Wilson can now make ultraviolet images of the cosmos
c.) New technologies will soon allow astronomers to use X-ray telescopes on the Earth's surface
d.) Thanks to interferometry, a properly spaced set of 10-meter radio telescopes can achieve the
light-collecting area of a single, 100-kilometer radio telescope
e.) All of the above are true
Answer: "a" is true. The others are false.
"b" is false because few ultraviolet photons are able to pass through the Earth's atmosphere and
adaptive optics have nothing to do with improving ultraviolet detections on Earth.
"c" is false because X-rays cannot travel far through the Earth's atmosphere and new technologies
cannot solve that essential problem.
"d" is false in concept -- interferometry allows us to achieve the angular resolution
(measured in terms of the diffraction limit) of a larger telescope by spacing the smaller
telescopes out. But, if you want to have the same light collecting area as a 100 km radio telescope,
you need to have area= pi*(50km)2. Each 5 meter telescope has pi*(2.5m)2 of area. So, in order
to have the same collecting area as a 100 km telescope, the number of 5 meter telescopes you
would need to connect is (50 km x 1000 m/km / 2.5 m)2 = i.e. 4 x 108. That isn't practical.
No, the advantage of using interferometry is a big improvement in angular resolution,
not a big improvement in collecting area.

7.) If our eyes don't see radio frequency light, how do astronomers make images of radio emission? Answer: The detectors can detect the brightness of objects in radio-frequency light. They can also detect the shape of the object. This information is stored. So that humans can work with the information, the stored information is translated into a visible-wavelength image. This can be done by color-coding visible colors to radio wavelengths (that makes a "false color" image).

8.) Which one of the following would be an example of a spectroscopic observation?
a.) Astrid, the astronomer wanted to study a particular optically thin gas cloud. Unlike the relatively bright Orion Nebula, her cloud was very dim. So, Astrid studied it by recording the light from a star located beyond the gas cloud and measuring how much 410nm, 434nm, 486nm, and 656nm light the gas cloud had absorbed.
b.) Astrid, the astronomer wanted to study a particular binary star system. Her binary star system was very far away and so she was not able to resolve the two stars in her photographs. So, Astrid studied it by recording the system's flux every minute over several weeks. She could see that the flux varied in a regular, periodic fashion.
c.) Astrid, the astronomer wanted to study the bubbles made by exploding stars. Since her favorite bubble was so faint, she had to put a filter on her telescope. She used a filter that only allowed 656 nm light to come through to the detector. From her observations, she was able to see the circular shape of the bubble.
d.) None of the above
Answer: a. In option a, Astrid is measuring and analyzing aspects of the spectrum (the emission lines) from the gas cloud. She is using that information to learn about the cloud. Option b is not right because it is a timing observation. Option c is really an imaging observation. The use of the filter to select a single color of light is really being done in order to make a better image, not to learn about the spectrum. In order to have a spectrum, you must have more than one color of light. But, Astrid has thrown away all the other colors of light in option c.

9.) When we look at the night sky, we see that the stars "twinkle". Why is that?
Answer: The Earth's atmosphere distorts the light coming from the star. It bends the light's path slightly. Because the air in the atmosphere moves constantly, the amount and direction of the bending changes constantly. You could say that the atmosphere behaves like a constantly changing lens which causes stars' light-rays to shift back and forth constantly.

10.) Which types of light (i.e. which wavelengths) cannot pass easily through the Earth's atmosphere.
Answer: Gamma rays, X-rays, most ultraviolet wavelengths (all but the longest ultraviolet wavelengths), most infrared wavelengths (all but the shortest infrared wavelengths cannot reach even the Earth's mountaintops).