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Conceptual Physics Study Notes & Questions: Week 13—EM Waves (Chap. 19) 1) An electromagnetic wave consists of interacting time-varying electric and magnetic fields. (p399) As described by Maxwell’s equations, a change electric field generates a magnetic field, and a changing magnetic field generates an electric field. This mutually-generating pair of force fields propagates through space at c, the speed of light, 3*108meter/sec (that is, to the moon and back in 2.6 seconds). 2) The intensities of these electric and magnetic fields vary sinusoidally, that is, they vary in time and space like a sine curve: growing ‘positively’, shrinking, reversing orientation, growing ‘negatively’, shrinking, reversing orientation again, etc. (see Figure 19-1). Like all force fields, these electric and magnetic fields are vector fields, that is, they have a direction to the push or pull they exert. The direction of these field changes occur perpendicular to the direction of their propagation. 3) Polarization: Given an xyz coordinate system, if the EM wave is traveling in the z direction, the electric field can vary along the x-axis and the magnetic field will vary along the y-axis, OR the electric field can vary along the yaxis and the magnetic field will vary along the x-axis. These are the two possible polarizations of the EM wave. There are special materials that will allow one sort of polarization to transmit while blocking the other polarization. This is a polarization filter and is important in laser technology and sunglasses, • When light reflects off a surface, one type of EM polarization reflects better than the other. Polaroid sunglasses reduce glare by cutting the dominant reflected polarization while allowing the other polarization to pass through. 4) The energy of an EM wave is quantized—that is, it’s energy comes packed in a unit, called a photon, that is absorbed or emitted by an atom as a single quantum of energy. A photon’s energy is related to its wavelength: Ephoton = hf, where f is the photon’s frequency, and h is Planck’s constant (h = 6.63*10-34 Joule-seconds). Even though a photon has no mass, it does have momentum, which can impart a push against a reflective surface: Momentumphoton = hf/c. 5) EM waves come in various forms depending on their frequency: radio, microwaves, infrared, visible, ultraviolet, X-ray and gamma rays. (p403).These families of frequency will be absorbed, transmitted or scattered by matter in different ways. (p402—414) 1 Conceptual Physics Study Notes & Questions: Week 13—Optics (Chap. 20) 1) Radiation interacts with matter in three basic ways (p419) a) Transmission—the EM wave passes through the material, however, the photon’s electric field drags on electrons and protons, slowing the EM wave’s speed. A material’s index of refraction indicates how much the material slows light (p428) b) Absorption—the EM photon is absorbed by the material c) Scattering—the EM photon interacts strongly with the matter, their wave functions mix momentarily and when they separate the photon is moving in a different direction. 2) Scattering is either diffuse—light scatters uniformly in all directions—or it is reflective in varying degrees. A perfectly reflective surface is a mirror, a partially reflective surface (such as a waxed car) is a specular reflector (p421). Both natural and man-made materials tend to have a mixture of diffuse and specular reflection. ‘Shiny’ material have more specular reflection, while ‘drab’ or ‘flat’ surfaces are much more diffuse. 3) A vector projecting straight out from a given surface is called the surface normal vector (or simply, the normal). For a reflective surface, the incident angle (the direction the light comes in, measured from the normal vector), is equal in magnitude to the reflection angle (the direction the light comes off, measured from the normal vector) (p421). 4) Concave mirrors (which belly in) focus light. Light rays coming from a large distance away, like from a star, get reflected and focused at a single spot called the focal point. The distance from the mirror to this focal point is called the focal distance (p422). Telescopes use concave mirrors to gather large areas of faint light rays and focus their combined intensities so distance stars and galaxies can be observed. Convex mirrors (which bow outward) disperse light rays, spreading them outward—the opposite of focusing. 5) Refraction is the change in light’s speed as it passes from one material’s index of refraction, to another’s. If the incident angle is not zero—that is, the incoming ray is not parallel to the normal of the boundary surface—the light ray’s direction bends at the boundary surface (p427). Figure 20-9 (p429) shows how a light ray’s refraction angle changes from its incident angle as it passes from a material with a low index of refraction, n1, into a material with a higher index of refraction, n2: if n1<n2, then angleincident > anglerefraction. On the other hand, if n1>n2, then angleincident < anglerefraction. 2 6) Refraction can be understood more easily if we discuss the wavefront of the incident light ray. Wavefront lines lie perpendicular to the direction of a light ray, aligned along the crest points of the EM wave’s electric field: Ray Wavefronts 7) When wavefronts enter a medium with a higher index of refraction, they slow. If they enter this medium at an angle, one part of the wavefront slows first, causing the overall direction of the ray to change (see Figure 20-8 on p429). 8) The boundary between two mediums’ indices of refraction does not have to be sharp, it can be a gradual change, such as the fuzzy boundary between hot and cold air. These soft boundaries cause light rays to curve instead of bend sharply(p431). Rays curve away from the faster medium, i.e. the material with the lower index of refraction. 9) Something special happens when a light ray from a high index material passes into a low index material. At a critical angle, the ray’s bend is so severe that it never leaves the first material but travels along the boundary surface (p425, Figure 20-6). At even larger incident angles the ray reflects off the surface, never leaving the first medium—we have total internal reflection. 10) Total internal reflection makes fiber optics work—once a ray travels along the inner core of a fiber, total internal reflection prevents it from leaving the fiber core. If there is very low absorption by the fiber’s material, a light ray can travel 100 kilometers. (p424). 11) Lenses are transparent materials, such as glass, that are carefully constructed to control refraction (p432). Convex lenses bulge in the center and have a focal point like concave mirrors—these are called converging lenses. Concave lenses are thinner in the center and cause light rays to spread out—these are diverging lenses. Complex lenses combine these simpler lenses to produce sharp images inside 3 a camera, telescope or microscope (p432). 12) A material’s index of refraction is wavelength dependent. That is, EM waves of different frequencies will slow and bend differently as they cross the material surface. Shorter wavelengths, such as blue light, bend more than longer wavelengths (such as red light). This wavelength dependence of refraction is called dispersion. 13) What we call white light is actually the mixture of light rays with many different wavelengths. Special glass shapes, called prisms, use dispersion to separate white light into its component colors—the colors of the rainbow (p434). 14) What are the 3 primary additive colors (p437)? What are the 3 primary subtractive colors? Why are they given these “additive” and “subtractive” names? Which are used in TVs? Which are used in book illustrations? 15) Why is the sky blue (p437)? Why are sunsets red? Why are clouds white? Are these caused by scattering or absorption? 4 Conceptual Physics Study Notes & Questions: Week 14—Quantum Mechanics (Chap. 22) 1) Atoms are small. Really small. Really, really small. Extremely tiny. 2) Strange things happen on very small size scales. Things sometime behave like particles (usually when they interact with other things), sometimes they behave like waves (usually when they are traveling). This is called waveparticle duality, and is the key feature of quantum mechanics. Though many day-to-day quantities seem continuous—things like solids, liquids, electricity, energy—at very small size scales we have found all of these things are quantized—that is, they come packaged in units or quanta. Solids and liquids are made of discrete atoms, electricity is made of electrons, and energy is packed in photons. It’s the quanta that puts the quantum in quantum mechanics (p472). 3) Uncertainty Principle: At the quantum scale, any measurement alters the object that is being measured (p474). One consequence of the this is that you can not simultaneously measure a particle’s position and speed at the same time: Dx Dp > h, Dx is the uncertainty in particle position, and Dp is the uncertainty in the particle momentum, and h is Planck’s constant. There is a similar relationship between measuring the energy of an event and its time duration: DE Dt > h. 4) The famous Schrödinger equation, relates the wave nature of a particle to the energy field around it. The solution to this equation is very complex and except for the simple hydrogen atom, it can only be approximated by digital computations. However, its approximate solution can be converted to a probability density function—describing where a particle is likely to be at any given moment (p478). 5) An important feature of the quantum world is that the wave function for an electron orbiting an atomic nucleus must be a standing wave—that is, the orbital circumference must be an integer number of electron wavelengths (for the electron in its potential energy field—created by protons in the nucleus and its neighboring electrons). (p484) This fact determines what orbital energy levels an electron can occupy in the atom. 6) Another important aspect of quantum mechanics is the Pauli Exclusion Principle. It means that no two electrons can occupy the same atomic orbital (and spin state). This principle makes chemistry and life possible. More on 5 this later… So small you can’t see them. Puence.