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Download Chapter 32Light: Reflection and Refraction
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Chapter 32Light: Reflection and Refraction HW 6: Chapter 32: Pb.12, Pb.43, Pb.46 Chapter 33: Pb.14, Pb.27, Pb.29 Due On Friday, April 14. 30-4 LR Circuits Example 30-6: An LR circuit. At t = 0, a 12.0-V battery is connected in series with a 220-mH inductor and a total of 30-Ω resistance, as shown. (a) What is the current at t = 0? (b) What is the time constant? (c) What is the maximum current? (d) How long will it take the current to reach half its maximum possible value? (e) At this instant, at what rate is energy being delivered by the battery, and (f) at what rate is energy being stored in the inductor’s magnetic field? 30-5 LC Circuits and Electromagnetic Oscillations An LC circuit is a charged capacitor shorted through an inductor. 30-5 LC Circuits and Electromagnetic Oscillations Summing the potential drops around the circuit gives a differential equation for Q: This is the equation for simple harmonic motion, and has solutions . . 30-5 LC Circuits and Electromagnetic Oscillations Substituting shows that the equation can only be true for all times if the frequency is given by The current is sinusoidal as well: 30-5 LC Circuits and Electromagnetic Oscillations The charge and current are both sinusoidal, but with different phases. 30-5 LC Circuits and Electromagnetic Oscillations The total energy in the circuit is constant; it oscillates between the capacitor and the inductor: Problem 34 34. (II) A 425-pF capacitor is charged to 135 V and then quickly connected to a 175-mH inductor. Determine (a) the frequency of oscillation, (b) the peak value of the current, and (c) the maximum energy stored in the magnetic field of the inductor. 30-6 LC Oscillations with Resistance (LRC Circuit) Any real circuit will have resistance added to the LC. 30-6 LC Oscillations with Resistance (LRC Circuit) Now the voltage drops around the circuit give 31-3 Maxwell’s Equations This set of equations describe electric and magnetic fields, and is called Maxwell’s equations. In the absence of dielectric or magnetic materials, they are: Gauss’s Law Gauss’s Law of magnetism A magnetic field induce a electric field General form of Ampere’s law A electric field induce a magnetic field 31-4 Production of Electromagnetic Waves Since a changing electric field produces a magnetic field, and a changing magnetic field produces an electric field, once sinusoidal fields are created they can propagate on their own. These propagating fields are called electromagnetic waves (EM). What is Light? https://www.youtube.com/watch?v=IXxZRZxafEQ Induced Electric Fields • Electric & Magnetic fields induce each other Changing B induces emf changing E Changing E changing B create electromagnetic waves Electromagnetic Waves Charge accelerates: this creates a changing B-field By Faraday’s Law of induction this creates a changing E-field E B 31-5 Electromagnetic Waves, and Their Speed, Derived from Maxwell’s Equations B and E are related by the following equation Calculated by Maxwell . Here, v is the velocity of the wave. The magnitude of this speed is around 3.0 x 108 m/s – precisely equal to the measured speed of light. Maxwell’s argue that light in EM wave after this calculation, Hertz showed this experimentally 8 years later. Speed of EM Waves -- vacuum • EM waves do not require a medium to propagate 1 m c= = 2.998 ´ 10 s Î0 m0 8 Permittivity of free space = 8.85 x 10-12 C2/Nm2 Permeability of free space: = 4 x 10-7 Tm/A 31-6 Light as an Electromagnetic Wave and the Electromagnetic Spectrum The frequency of an electromagnetic wave is related to its wavelength and to the speed of light: Speed of Light in matter • Generally light slows down when it encounters a medium other than vacuum. v = n is the index of refraction of the medium n≥1 c n c = lof v = lf l= v c lo = lo n l l c l v Frequency is unchanged n 31-6 Light as an Electromagnetic Wave and the Electromagnetic Spectrum Electromagnetic waves can have any wavelength; we have given different names to different parts of the wavelength spectrum. 32-1 The Ray Model of Light Light very often travels in straight lines. We represent light using rays, which are straight lines emanating from an object. This is an idealization, but is very useful for geometric optics. 32-2 Reflection; Image Formation by a Plane Mirror Law of reflection: the angle of reflection (that the ray makes with the normal to a surface) equals the angle of incidence. 32-2 Reflection; Image Formation by a Plane Mirror When light reflects from a rough surface, the law of reflection still holds, but the angle of incidence varies. This is called diffuse reflection. 32-2 Reflection; Image Formation by a Plane Mirror With diffuse reflection, your eye sees reflected light at all angles. With specular reflection (from a mirror), your eye must be in the correct position. 32-2 Reflection; Image Formation by a Plane Mirror What you see when you look into a plane (flat) mirror is an image, which appears to be behind the mirror. 32-2 Reflection; Image Formation by a Plane Mirror This is called a virtual image, as the light does not go through it. The distance of the image from the mirror di is equal to the distance of the object from the mirror d0 32-2 Reflection; Image Formation by a Plane Mirror Example 32-1: Reflection from flat mirrors. Two flat mirrors are perpendicular to each other. An incoming beam of light makes an angle of 15° with the first mirror as shown. What angle will the outgoing beam make with the second mirror?