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Physics 200 Class #5 Notes September 21, 2005 Reading Assignment Text: Chapter 3,4 pp. 59-94 Continuation of Chapter 2 Class Exercises Introduction to Chapter 3 Chapter 2 Newton’s particle Theory May or may not be covered in class, depending on timing. It's interesting in that it presents a hypothesis being made and being tested. (pp. 33-47; 47-56 is an interesting historical perspective on Newton) Chapter 3 A wave theory of light 3.1 Waves Whatever the nature of light may be, light is not like a tiny baseball. What else travels through space carrying information (energy)? A wave is a pattern, not a thing (like a ball). Usually a wave is a moving, changing pattern. or A wave is a disturbance that carries information (energy) from one point in space to another without the net motion of matter. What is the nature of the disturbance? In Chapters 3 and 4, we explore the properties of waves and learn that light has a wave-like character. In Chapter 5, we address the nature of the disturbance in the light wave. There are two extremes for wave motion: Transverse waves: The vibration is at right angles to the direction in which the wave is moving. (String waves, water waves, light) Compressional (Longitudinal) waves: The vibration is parallel to the direction in which the wave is moving. (Sound) 3.2 Some general properties of waves Reflections and variation in speed Phy 200 Fall 2005 Class_5 Page 1 of 8 Superposition The superposition principle: To get the resultant pattern during overlap, add the original patterns algebraically Phy 200 Fall 2005 Class_5 Page 2 of 8 Phy 200 Fall 2005 Class_5 Page 3 of 8 Periodic Waves The basic type of wave motion that we shall study is a periodic wave based on Simple Harmonic Motion. If we look at the individual elements in time, we get the following behavior (for example, the motion of a mass on a spring): Period (T): The time for one complete vibration. Frequency ( f ): Number of vibrations per second (oscillations per second or Hertz) If each point of the wave oscillates with this simple harmonic motion of Period T (frequency f 1/ T ), then a snapshot picture of the wave in space is shown in Figure 3.6. Then the wave moves a distance λ during a time of one period (T). The speed of the wave is: 1 v or since f v f NOTE T T following figure from http://eosweb.larc.nasa.gov/EDDOCS/Wavelengths_for_Colors.html#red Phy 200 Fall 2005 Class_5 Page 4 of 8 Some common frequencies and wavelengths. Given the wavelengths, what are the frequencies and vice-versa? Use v = 3 x 108 m/s as the velocity of light (also denoted "c"): c = f Microwaves: ~1 cm FM Radio: 100 MHz AM Radio: 100 kHz (The same percentage bandwidth (say plus or minus 1 percent) is a much smaller frequency range. Less information can be transmitted. Do you notice the difference in sound quality?) Visible light: Violet: 400 nm, Red: 650 nm Phy 200 Fall 2005 Class_5 Page 5 of 8 What a python or rattlesnake may see! Infrared view: http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Intro/ProfinIR.gif Flower markings on coneflowers (a) in ordinary light and (b) in ultraviolet light. (From Stern, Introductory Plant Biology, 8th ed., ©2000 McGraw-Hill Companies, Inc.) What a bee may see. Ultraviolet view Phy 200 Fall 2005 Class_5 Page 6 of 8 How do we transport energy? Particles: A particle is a discrete (localized mass) that can transport energy from one point to another; {Later, we will show: KE 12 mv 2 } Waves: A wave is a disturbance that carries energy (and momentum) from one point in space to another point in space without the net motion of mass from one point to another. There are two extreme types of waves: Transverse (strings and light) and longitudinal or compressional (sound). Later we will verify that light is a transverse wave (polarization). On the internet, see http://www.geocities.com/CapeCanaveral/Hall/6645/lontra_e/lontra_g.htm for example Guiding Principles: I Waves move at a constant velocity that is determined by the medium that supports them, rather than the waves themselves. (Note: light propagates in a vacuum and the speed depends on the electric and magnetic properties of free space.) II Waves obey a superposition principle. If two or more waves arrive simultaneously at the same point in space, the resulting effect is simply the sum of the effects of each of the waves. We look at examples of the latter in Chapter 4. If each point of the wave oscillates with this simple harmonic motion of Period T (frequency f 1 / T ), then a snapshot picture of the wave in space is: Then the wave moves a distance λ during a time of one period (T). The speed of the wave is: 1 v or since f v f T T We usually reserve the symbol c for the speed of light. Aside Note: The description of the wave in the previous figure can be written mathematically as: 2 y A sin x Phy 200 Fall 2005 Class_5 Page 7 of 8 For sound waves, we generally associate f with pitch. For light, this corresponds to color. We will eventually concentrate on the electromagnetic spectrum (light). 3.3 Light as a wave? This Section is best done by observing the phenomena using a ripple tank. 3.4 Refraction quantitatively inc vregionof incident wave f inc sin i AB inc sin r refr refr f refr vregionof refracted wave AB Comparison with light v sin i air sin r vwater Foucault showed: vwater vair but didn't know value vair 1.33 vwater Angle measurements confirm the wave prediction (and speed measurements)! But there is more! Michelson (1883) showed: We know that waves participate in interference and diffraction phenomena. The question we need to address is whether or not light participates in these phenomena. Phy 200 Fall 2005 Class_5 Page 8 of 8