Wave motion and Electromagnetic Radiation
The study of wave motion is important to physics because everything we see or hear travels via a wave; therefore all visual or auditory observations are interpretations of a wave. As I teach wave motion to my students, I want to make certain that they completely understand the physical concepts about wave motion. A wave is created when you drop a pebble into a pond and the wave will spread outward. If a leaf is floating on the surface of the pond, as the ripples of the wave pass, the leaf will move up and down. The leaf only moves up and down, not sideways. The water is not moving past, the wave is moving. Wave motion is the transfer of energy not matter. (Rothman, 1995) In wave motion, the relationship between the wave speed, v, the frequency of the wave, f, and the wavelength, Λ , is call the wave equation and is v = f Λ . Light or electromagnetic radiation is the form of wave motion that our eyes can perceive. Electromagnetic radiation or light has a constant speed in a vacuum and is equal to 3.00 x 10 8 m/s or, c, the speed of light. Our eyes have very limited vision and only respond to electromagnetic vibrations that have wavelengths between 0.0007 and 0.0004 of a centimeter long. We are constantly being bombarded by all other kinds of electromagnetic waves; they vary in size with some as small as atoms, called gamma rays, and others as large as mountain, known as radio waves. Electromagnetic waves come from the far reaches of the Universe and within our own bodies, and from the radio transmitter twenty miles away. I can "see" or know these waves are in the room because I can turn on the radio or TV and tune into their frequencies and I will suddenly be able to see or hear them. If I had other types of detectors I could sense other signals. I can sense some parts of the infrared radiation as heat on my skin. (Cole, 1999)
In the past, when teaching my students about electromagnetic wave theory, I have limited the scope to the basic concepts of reflection, refraction and geometric optics. I would teach the physics, but limit the application to the optics of glasses for corrective vision and observation related to reflection and refraction. In my curriculum unit I will include information on the study of light and electromagnetic waves to explore the distant galaxies. The inclusion of such modern astronomy and cosmology will hopefully help students make connection to the reason why an understanding of wave motion and electromagnetic radiation is important to the study of how the Universe was formed, and the composition of stars.
Spectral Analysis
In the early 1800s the French philosopher Auguste Comte argued that because the stars are so far away, humanity would never know their composition. He stated that we already knew every thing we were going to know about starlight, yet just a few years later scientists began applying spectral analysis to starlight to learn the very things that Auguste Comte had deemed unknowable. We now know that atoms of each chemical element emit and absorb light at a unique set of wavelengths, like a chemical fingerprint. We also have learned that the motion of a light source also affects wavelengths, permitting us to deduce how fast stars and other objects are approaching or receding from us. Scientists now know that most of the Universe is composed of Hydrogen and Helium and the assembly of elements on our Earth is unusual. In this curriculum unit I will add information about Kirchhoff Law's on the spectrum of the Sun, and describe the Doppler Effect as it is related to the motion of stars and galaxies. I want to add information to the study of telescopes to include a discussion on the various types of telescopes in use today, and explain the Hubble equation and how it is used to determine the age of the Universe.
In 1814 Joseph von Fraunhofer repeated Newton's classic experiment of shining a beam of sunlight through a prism. His result was different in that Fraunhofer found the solar spectrum contains hundreds of fine, dark lines, now called spectral lines. Almost fifty years later, chemists discovered that they could produce spectral lines in the laboratory and use these spectral lines to analyze what kinds of atoms different substances are made of. Kirchhoff and Bunsen found that each chemical element produces its own unique pattern of spectral lines and the identification of chemical substances by their unique patterns is called spectral analysis. The spectrum of the Sun, with its dark spectral lines superimposed on a bright background may seem to be unrelated to the spectra of bright lines against a dark background produced by substances in a flame test taught in chemistry class. Kirchhoff's conclusions about spectra are summarized in three important statements about spectra that are called Kirchhoff's laws. These laws are as follows; the first is that, a hot opaque body, such as a perfect blackbody, or a hot, dense gas produces a continuous spectrum, which is a complete rainbow of colors without any spectral lines. The second is that, hot, transparent gas produces an emission line spectrum- a series of bright spectral lines against a dark background. The third law is that, a cool, transparent gas in front of a source of a continuous spectrum produces an absorption line spectrum- a series of dark spectral lines among the colors of continuous spectrum. Furthermore, the dark lines in the absorption spectrum of a particular gas occur at exactly the same wavelengths as the bright lines in the emission spectrum of that same gas. The truly remarkable result in the study of spectroscopy is that it can determine chemical composition at any distance, and by using the principles outlined by Kirchhoff's laws, astronomers have the tools to make chemical analysis of objects that are at almost inconceivable distances to determine the nature of celestial objects. (Freedman and Kaufmann, 2005)
Doppler Effect
In addition to knowledge of the composition of stars the study of the effect of motion on the wavelength, or Doppler Effect, will be included in the curriculum unit. All introductory physics curriculum include problems and discussion about the Doppler Effect in sound waves. I want to include information and problem sets on the Doppler Effect on light waves emitted from distant stars and galaxies. The Doppler Effect is an important tool in astronomy because it uncovers basic information about the motion of planets, stars and galaxies. For example, the rotation of the planet Venus was deduced from the Doppler shift of radar waves reflected from its surface. Astronomers use the Doppler Effect along with Kepler's third law to measure the masses of galaxies. The Doppler shift was used on the second landing on the Moon to give a much more precise landing trajectory. The first landing on the Moon was four miles away from its target point, but by using the Doppler shift in radio signals from the lunar module in lunar orbit scientist landed the Apollo 12 within ten yards of its intended landing point. (Chaikin, 1994)
We have all noticed the Doppler Effect for sound waves. When a fire truck is approaching, the sound wave from its siren has a shorter wavelength and higher frequency than if the sound was at rest, and hence you hear a higher pitch. After the fire truck passes you and is moving away, you hear a lower pitch from the siren because the sound waves have a longer wavelength and a lower frequency.
When studying the Doppler shift from a light source from distant stars there is a red or blue shift in the color. The red-shifts and blue-shifts of stars visible to the naked eye, or even through a small telescope, are only a small fraction of a nanometer. These tiny wavelength changes are far too small to detect visually. The Doppler shift in stars was not detected until, 1890, fifty years after Doppler's original discovery. If the wavelength of a particular spectral line from a light source that is not moving is Λ o. If the source is moving the wavelength shift is ΔΛ. Where ΔΛ = Λ - Λ o the Doppler shift equation for light is
ΔΛ/Λ o = v/c
Where v is the velocity of the source measured along the line of sight and c is the speed of light, 3.00 x 10 8 m/s. The velocity determined from the Doppler Effect is called the radial velocity, because v is the component of the star's motion parallel to our line of sight, or along the radius. I will include in the Doppler problem set problems that determine the radial velocity of stars and galaxies and the Doppler wavelength shift. (Rothman, 1995)
Telescopes
To observe the Doppler Effect in stars and galaxies the power of the telescope and the use of telescopes that view light outside the visible range had to be developed. My curriculum unit will include discussion of the development of telescopes and include pictures from various telescopes of distant celestial objects. The first optical telescope was invented in the Netherland in the early 17 th century. Soon after, Galileo used one for his ground breaking astronomical observations. The first telescopes used glass lenses to refract light to make bright objects appear larger and brighter. The light gathering power of a telescope is directly proportional to the area of the objective lens, therefore doubling the diameter of the objective lens results in a increase in power of the telescope of four times. For example, the Lick refracting telescope in California has a 90 cm objective lens and Galileo's telescope of 1610 had a three centimeter objective lens. The Lick telescope has a 30 times larger lens and a 900 times greater power to gather light than Galileo's telescope. The major drawback in using a refracting telescope is that any defect in the glass with which the lens is made will create poor quality images. In addition to defects causing poor image quality, refracting telescopes also have problems with chromatic aberration. Variation in the index of refraction in glass is responsible for the rainbow of color when light passes though a prism. Chromatic aberration is the variation in focal length due to the variation in index of refraction due to frequency of the light.
In 1663, James Gregory first proposed a telescope using reflection from a concave mirror. Reflecting telescopes have many advantages over a refracting telescope, the major being that defects within the glass have no effect on the optical quality of the image, and there is no chromatic aberration. One of the problems with reflecting telescopes is that the focal point is in front of the objective mirror. When you try to view the image formed at the focal point your head will block part or all of the light reaching the mirror. In 1668, Newton simply placed a small flat mirror at a 45 o angle in front of the focal point which deflects the light ray to one side where an eye piece lens is placed to magnify the image further. A reflecting telescope must be designed to minimize a defect called spherical aberration. Spherical aberration occurs when different parts of a mirror have difference focal lengths and result in a fuzzy image. Light from the city also degrades telescope images. Light pollution illuminates the sky, making it more difficult to see the stars. To avoid light pollution, observatories are built in remote locations far from any city lights. The best location for a telescope is in orbit around the Earth, where it is unaffected by weather, light pollution or atmospheric turbulence.
Imaging of the distant objects began in the nineteenth century with the invention of photography. Long exposure images of objects from a telescope can reveal details in galaxies, star clusters and nebulae that would not be visible to an astronomer by looking through a telescope. Unfortunately, photographic film is not very efficient; most of the light that falls on photographic film is not recorded. The most sensitive light detector currently available to astronomers is the charge-coupled device (CCD). A CCD is a semiconductor material divided into an array of small light-sensitive elements called pixels. Compared to photographic film CCDs are about 35 times more sensitive to light and respond to 70% of the light falling on them versus 2% for photographic film. (Freedman and Kaufmann, 2005)
Hubble Law
When astronomers observe new objects in the heavens the first study they do is attach a spectrograph to a telescope and record the spectrum. Vesto M. Slipher, working at Lowell Observatory in Arizona, discovered that of the fifteen spiral nebulae he studied, eleven of the spectral lines showed a Doppler shift toward the red end of the spectrum indicating all were moving away from the Earth. The marked dominance of the Doppler red shift revealed a basic law of our expanding Universe (Freedman and Kaufmann, 2005).
During the 1920s, Edwin Hubble and Milton Humason concluded that most galaxies show a red-shift in their spectrum, and there is a direct correlation between the distance to a galaxy and its red-shift. The correlation is stated as "the more distance a galaxy, the greater its red-shift and the more rapidly it is receding from us." (Freedman and Kaufmann, 2005) Hubble estimated the distance to a number of galaxies based on the red-shift and he found that the red shift, z, is determined by the following relationship
z = (Λ-Λ o)/Λ o = ΔΛ/Λ o
From the red-shift data, Hubble used the Doppler formula to calculate the speed at which these galaxies are receding from us. He found that the recessional velocity of a galaxy, v had a linear relation to the distance to the galaxy and published this discovery, which is now stated as the Hubble law, the relationship in equation form is
v = H od
Where v, is the recessional velocity, d is the distance and H o is the Hubble constant and is the slope of the linear relationship and equal to 71 km/s/Mpc (71 kilometer per second per megaparsec). (Freedman and Kaufmann, 2005)
My curriculum unit will end with the discussion of the red-shift and Hubble Law relationship. The students will work several problems using the Hubble Law to determine distances to other galaxies. In my curriculum unit, the students began the study of space within the physics curriculum with calculations of the distance to the Sun, and planets based on the speed of light. They also calculated time to travel through our Solar system. Student applied Newton's Laws to determine the forces and escape velocity to leave and return safely to the Earth's surface and speed to stay in a stable satellite orbit. Students designed and build their own bottle rockets.
I added to the physics curriculum information about spectral analysis of distant objects in space and introduced Kirchhoff's laws. I expanded the study the Doppler Effect to include problems and study on the red-shift of light. There is a unit on various types of telescopes. The unit will include images from the various types of telescopes and discuss the importance of viewing other parts of the electromagnetic spectrum. The curriculum unit will end as it started, by calculating distances and velocity, but not of near objects but of the most distant objects in the Universe using the most recent information on the Doppler shift and the Hubble equation from the spectrum of light from distant galaxies.
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