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Transcript
Physics 200 Class #8 Notes October 3, 2005 Reading Assignment for Wednesday Text: Chapter 5 pp. 106-118 Finish interference Review of Electric Forces (Charge) Introduction to Electric and Magnetic Fields Finishing up interference: thin film interference Thin Film Interference You get a reflection off the front surface (ray 1) and off the back surface (ray 2) of the thin film. For normal incidence (incident angle equals zero degrees): The geometric path difference is 2d Note that the wavelength in the material is different than the wavelength in air. ' =/n So if the total path difference is equal to 1 wavelength ('), you have both ray 1 and ray 2 in phase and you get constructive interference. A bright area. Mathematically, you get constructive interference when: 2d = ' Really, this works for 2 wavelengths, 3, 4, etc., so using "m" to stand for any integer. 2d = m' for constructive interference. Skip ahead to Electricity and Magnetism if you don't want any more details on thin film interference. Now, since we are dealing with materials with different indices of refraction, we have to remember that when light reflects, there is sometimes a 180 degree phase change. If the material it bounces off of has a higher index of refraction than the material it has been traveling in, then you get that phase change, or "phase flip" as it may be called. In air (n=1.003), light bouncing off of an interface with a piece of glass (n=1.5) will have the phase flip. In oil (n=1.5 for example), light bouncing off of a blob of water (n=1.33) WILL NOT. You see? Now apply this to mica (n=1.6) and air (n = 1). Phy 200 Fall 2005 Class_8 Page 1 of 4 So, in the air/mica/air example in the diagram, the light off the front of the mica (air to mica interface) will flip. The light that travels through the mica and bounces off the back surface (mica to air interface) will not. So with one phase flip: 2d = m' for destructive interference. If you had diamond stuck on the right side of the mica, so you had a mica-to-diamond interface (ndiamond = 2.42) the bounce off that second interface would also have a phase flip. Then both reflected rays having the same phase shift and you'd have constructive interference with 2d = m' That may be alot to remember, but remember that you have light bouncing off of both surfaces of a thin film and that causes interference. And since it's wavelength dependent, you get different colors interfering differently. Now the pretty part Since wavelength is in that equation, you get different interference for different colors. Look at a slick of oil on a wet road. This is just thin film interference. from http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/phopic/gaspot.jpg Now - electricity and magnetism Contributions of Ben Franklin (1706-1790) and Charles Coulomb (1736-1806) Source of Electric phenomena: Electric Charge (positive and negative) (We now know that Electric charge is “quantized” that is it comes in integer multiples of a fundamental unit-the charge on the electron.) Phy 200 Fall 2005 Class_8 Page 2 of 4 Like Charges Repel Unlike Charges Attract Demonstrations: Charging by Friction - fur (becomes +) and vinyl (becomes -) Ben Franklin first categorized charge as + and -. The negative one (electrons) happens to be the one that does most of the moving, we later found out. Charging by Scotch Tape Induced charges Why does the balloon stick to the wall? Insulators: cork, glass, rubber Conductors: metals Conservation of Electric Charge: Electric Charge cannot be created or destroyed it can only be transferred from one object to another. The total amount of charge in the universe is constant. Force: Push or Pull And (in this case) grows weaker with distance - watch how much the fur moves. And depends on how much stuff you have: mass (for the gravitational force) or charge (for the electric force) The Electric Force (Coulomb’s Law) qq FE k 1 22 d q1 and q2 are in Coulombs (a rather large unit; The charge on the electron is 1.6 x 10-19 C.) d is in meters FE is in newtons k is a universal constant and must carry units: k = 9 x 109 N m2/C2 Comparing the Electric and Gravitational Forces: The forces between an electron and a proton in the hydrogen atom: 31 2 M eM p kg)(1.7 x 10 27 kg) 11 N m (9.1 x 10 FG G 6 . 7 x 10 3.7 x 10 47 N r2 kg 2 (5.3 x 10 11 m) 2 FE k Qe Q p r2 9 x 10 9 N m 2 (1.6 x 10 19 C )(1.6 x 10 19 C ) 8.2 x 10 8 N 2 11 2 C (5.3 x 10 m) FE is 10 39 times stronger Note the similarity to the gravitational force. This is in general difficult to handle mathematically and is also “action at a distance”. Enter Faraday with his “Electric Field”. The field concept is an attempt to get around the “action at a distance” force. q force E k 22 with a direction given by the force on a charge q1 r Then: F q1 E Phy 200 Fall 2005 Class_8 Page 3 of 4 The units for E must be newtons/coulomb ****************************************************************** Demonstrations It is difficult to visualize the static electric field, but we can easily visualize a magnetic field and we will do this shortly. We can demonstrate the energy contained in the electric field by using the Van deGraaff Generator or by charging a “capacitor”. Representing the Field: We represent the field by drawing arrows giving the direction and strength (length) at each point in space surrounding a charge. It is not reasonable to draw too many arrows since the picture would soon become too complicated. It is conventional to simply draw one long arrow away from a positive charge. Keep in mind that the field gets stronger as we approach the charge. E points away from positive charges and towards negative charges. Examples: See text Magnetic Fields It is easy to visualize the magnetic field lines around a bar magnet using iron filings. Now the question is: How do we find the force on a charge? Experiments show that the force on a stationary charge is zero and the force on a moving charge is: F qvb if v is perpendicu lar to B plus a direction given by the right hand rule! F qvB sin( angle between v and B) Phy 200 Fall 2005 Class_8 Page 4 of 4