Chapter 33 Light Waves
How do light waves differ from waves on a string, water waves, sound waves?
Huygens was a contemporary of Newton. Huygens believed light traveled as a wave. Newton believed light was made of particles. Who was right?
page 2 Superposition of Circular Wave Patterns *What is "superposition?"
The photographs were made by shining a small light on a tank of water. The waves in the water cast shadows that are seen in the photographs. The bright line is the crest (peak) of a wave. The dark region is the trough (valley) of the wave. Figure 1 a,b: Does it seem to you that the waves move out in all directions from the source of the wave?
Figure 2 a,b,c: Two wave sources are in use in these figures. The waves constructively and destructively interfere.
*Define "constructive interference." (Use the terms peak and/or valley.)
*Define "destructive interference." (Use the terms peak and/or valley.)
Figure 2a shows destructive interference along the line of nodes.
page 4 Huygens’ Principle
The front edge of a wave is called the wavefront. In Figure 3 a parallel set of wavefronts strike a barrier that has a narrow opening. You can see that the waves spread out as if the opening was a source of waves. The same pattern is created if the opening is located above or below the position used to take the photograph of Figure 3. Huygens proposed that the next position of the wavefront could be found by letting each point on the current wavefront emit a semicircular wave.
Figure 4 shows a circle emitted by every point on the current wavefront. This is OK if you want to check that the previous wavefront is in the correct position. We will only use the forward moving portion of the circles shown in the text. This semicircular wave expands a distance given by multiplying the speed of the wave by the time interval desired. The most distant portions of these semicircles locates the new wavefront. The dashed line in Figure 4 is the location of the new wavefront.
Imagine that a distant flashlight is shining on left side of the barriers in Figures 5 through 8. The light arrives at the barrier in parallel wavefronts. The case of the smallest opening shows the largest amount of wave motion in directions different from the direction of the incoming light.
* This spread of direction as light passes the edge of an opening is called "diffraction."
*Why don’t we observe diffraction for light passing through a door or window?
page 6 Two Slit Interference Pattern
With two openings in the barrier we see constructive and destructive interference from the two waves. The ripple tank of water allows us to see the waves in transit. With light we only see the light as it hits a screen some distance away from the two slits.
*In Figure 10, where would the most erosion of sand on the beach occur:
a) at position A or b) at position B?
The location on the screen where the two waves constructively interfere is called the central maximum. The interference pattern is symmetric on the two sides of the central maximum. The first minimum (destructive interference) occurs on both sides of the central maximum. Then the next location of constructive interference is labeled the First maximum.
Suppose, as is shown in Figure 10, that the wavefronts reach the two openings at the same time. Both waves travel with the same speed toward the beach.
Why is there destructive interference at the first minimum position?
Why is there constructive interference at the first maximum position?
page 8 First Maxima
Figure 12: Why is the point on the screen labeled the "first maximum?"
Why are there 11 peaks for the wave that left the bottom opening and only 10 peaks for the wave that left the top opening?
Make your own sketch of Figure 12 that
shows the two openings and the two
dashed lines going to the first maximum
position on the screen. Label the distance
from the middle of the top opening to the
middle of the bottom opening, d. Draw a
right triangle similar to the right triangle
shown in Figure 13. Theta is the label for
the angle at the top of your right triangle.
Verify equation 1.
Let Y be the distance along the screen from the central maximum to the first maximum. Let the distance from the openings to the screen be labeled D. Write an equation that relates D, Y and tan(theta).
page 33-10 Two Slit Pattern for Light
The debate over whether light travels as particles (Newton’s view) or light travels as a wave (Huygen’s view) was not experimentally settled until 1801. Young’s double slit experiment demonstrated interference of the waves from two openings and verified that light travels as a wave. The double slit experiment required that the wavefront from one wave strike both openings at the same time. I will award one bonus point to the person who is first to send me email with the correct answer to this question: How did Young set up the experiment to meet the requirement that the wavefront from one wave reach both openings at the same time?
I will set up a laser and double slit so you can see an interference pattern similar to the one in the text.
We will do the calculation on page 11 in a slightly different way.
page 12 The Diffraction Grating
A diffraction grating uses the interference effect to produce narrower maxima on the screen than just two slits. Why would multiple slits produce narrower maxima?
Why are the maxima at the same locations for the double slit and the diffraction grating (given that the wavelength, slit separation, and distance to the screen remain constant)?
page 14 More About Diffraction Gratings This will be summarized in class.
page 15 The Visible Spectrum What colors can you see?
What is "white" light?
When white light passes through a diffraction grating, which color has the largest angle to the first maximum?
A common unit of measurement for visible light is the nanometer. The approximate range of visible wavelengths is from 400 to 700 nm. Figure 23 puts visible light into perspective regarding its relationship to the whole range of wavelengths for the electromagnetic spectrum.
page 16 Atomic Spectra Now that we have a tool for separating light into various colors we can study light emitted by various atoms.
DEMO We will look at the spectra of various atoms using handheld spectroscopes. The spectroscope uses a diffraction grating to separate the various colors of light.
*What was the first evidence for the existence of the element helium? Be specific.
The spectra from stars and galaxies can give astronomers information on the nature of the object. The light contains clues as to the elements present, the density of the material, the temperature of the material, the speed of the object emitting the light, and the magnetic field of the object emitting the light. The combination of photography and diffraction gratings led to major advances in astronomy in the late 1800’s.
The study of light from atoms in laboratory experiments has provided physicists with clues on the nature of the atom. The nature of the atom will be discussed further in Chapter 35. The spectra of light emitted by atoms is in disagreement with the predictions of Classical Physics. The Modern Physics model for atoms matches the data of the atomic spectra.
page 17 The Hydrogen Spectrum
The hydrogen gas tubes we use have low density hydrogen gas in the tube. The hydrogen atoms become excited (have extra energy) when electric power is applied to the tube. The atoms can give off light (photons) to shed this extra energy.
With simple equipment one can easily see three spectral emission lines for hydrogen. Figure 26 shows the emission spectrum from a low density hydrogen gas. The alpha line is red, the beta line is blue and the gamma line is violet.
*I will award one bonus point to the first person to send me email with the correct answer to this question: Why is the hydrogen alpha line the brightest? The answer is not in our textbook.
page 29 The Balmer Series
Figure 28 shows the Balmer Series of absorption lines for a particular star. This photograph is a negative print. Absorption lines are actually dark lines when this spectrum is viewed. We are only interested in the hydrogen lines. They are labeled with H9, H10 etc. What do you notice about the spacing of the lines as you look towards the left side of the photograph?
*Why is this set of lines called a series?
In 1885 Balmer found an empirical formula that predicted the wavelengths of the lines of the Balmer Series. What is an empirical formula? What is the smallest allowed value for m in equation 6?
Use m=4 and calculate the predicted wavelength. How can you verify that your calculation was correct?
page 20 The Doppler Effect
Have you ever been stopped at a railroad crossing when a train was approaching with its horn sounding? Describe the pitch (frequency) of the horn when the train is approaching you compared to the pitch of the horn when the train is moving away from you. The change in frequency due to the relative motion of the source and observer is known as the Doppler effect. The Doppler Effect can be used to calculate the speed of approach or recession of a source or of an observer.
Equations 9a and 9b show us how to calculate the observed wavelength for the case of the source moving or the observer moving with the source at rest. Equations 10a and 10b show us how to calculate the period of a wave for both cases. Write the set of equations that tells us how to calculate the new frequencies for each case.
We will do some calculations with these formulas.
page 21 Stationary Source and Moving Observer
I will give you the Doppler equations for this situation.
page 22 Doppler Effect for Light
When there is relative motion towards or away for a source of light and an observer there is a Doppler Effect on the frequency of the light.
Calculate the new wavelength due to the Doppler shift for the case of 450 nm light emitted by a star moving towards the earth at 200 km/sec.
page 23 Doppler Effect in Astronomy
Is the sun moving towards or away from any star? Is our galaxy moving? Are other objects in the universe moving? How would you know?
page 24 Red Ship and the Expanding Universe
Soon after Einstein developed the General Theory of Relativity, Einstein found that the equations did not describe a static (constant size) universe. Astronomers before 1920 believed that the universe was static. If gravity is universal should the universe fall inward towards some center? Einstein added a term (the "Cosmological Constant") to the equations that allowed the universe to be static. This term represented a counterbalancing force to gravity. In the 1920’s Hubble discovered that almost all galaxies have their light shifted towards longer wavelengths (red). The combination of distance determinations of those galaxies and calculations using the Doppler Effect show that the farther a galaxy is away from us the faster it is moving.
What questions do you have on pages 24 and 25?
Big Bang This is a misleading name. It was an expansion of hot material, not an explosion in the ordinary use of the word explosion.
page 26 A Closer Look at Interference Patterns
The wave nature of light is evident even when light passes through a single slit. But the slit needs to have a size on the order of the wavelength of light in order for the diffraction effect to be noticeable. I will give you the equation for calculating the positions of the minima.
Let light pass through a double slit. What would you see on the screen for a location in which the single slit equations predict a minimum but the double slit equations predict a maximum?
We will skip pages 29 and 30.
Copyright© 2001 - 2006 by Greg Clements Permission is granted to reproduce this document as long as 1) this copyright notice is included, 2) no charge above photocopy costs is made, and, 3) the use is for an educational purpose. Editing of the document to suit your own class style and purposes is allowed