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4/5/2017 AP PHYSICS 2 MECHANICAL WAVES UNIT 7 Quantum Physics, atomic, and nuclear physics CHAPTER 24 Electromagnetic Waves MECHANICAL WAVES MECHANICAL WAVES Polarization of waves Polarization is a property of waves that describes the orientation of the oscillations of the wave. Transverse waves can be polarized Longitudinal waves cannot be polarized 1 4/5/2017 Testing the polarization of light waves Polarization shows that light phenomena can be better explained by a transverse wave model ELECTROMAGNETIC WAVES A wave that DOES NOT require a medium through which to travel. Models that tried to explain how light propagate through air (outdated models) 1. Light is a mechanical vibration that travels through an elastic medium. This medium is completely transparent and has exactly zero mass. This medium is called ether. 2. A light wave is some new type of vibration that does not involve physical particles vibrating around equilibrium positions due to restoring forces being exerted on them. Discovery of electromagnetic waves In 1865, Maxwell suggested a new field relationship: a changing electric field can produce a magnetic field. This magnetic field was first detected in 1929, but was not measured precisely until 1985 due to its extremely tiny magnitude. 2 4/5/2017 Maxwell's equations Maxwell's equations 1. Stationary electric charges produce a constant electric field. D = v 2. There are no magnetic charges (no magnetic monopoles). B = 0 3. A magnetic field is produced either by electric currents or by a changing electric field. xE = 4. A changing magnetic field produces x H = an electric field. +J Maxwell's equations CONSEQUENCES OF MAXWELLS EQUATIONS Producing an electromagnetic wave A changing electric field can produce a changing magnetic field, which in turn can produce a changing electric field, and so on. This feedback loop does not require the presence of any electric charges or currents. CONSEQUENCES OF MAXWELLS EQUATIONS Vacuum permittivity and the speed of light Testing Maxwell’s Equations Henry Hertz (1857 – 1894) The constant εo is the vacuum permittivity: The constant μo is the vacuum permeability. k = 9x109 Nm2/C2 μo = 4 x10-7 N/A2 WHITEBOARD Show magnitude of v Show unit analysis Switch connects a charged capacitor to a the primary coil of a transformer (transmitter). Capacitor discharges, potential difference across the primary coil induces a huge potential difference across the secondary coil. Metal spheres charged and generated a spark 3 4/5/2017 Testing Maxwell’s Equations Henry Hertz (1857 – 1894) Henry Hertz: Testing the hypothesis that light can be modeled as an electromagnetic wave Hertz characterized the wave nature of electromagnetic disturbances by performing experiments similar to those used to determine the wave nature of visible light. For example, he observed reflection, refraction, and diffraction. The spark would indicate a large electric field between the spheres of the transmitter. The changing electric field produces an electromagnetic wave. When the wake reaches the receiver, it induces and electric current causing a weak spark. He also performed a double-slit experiment and observed interference. Antennas are used to start electromagnetic waves Antennas are used to start electromagnetic waves He observed polarization and measured their speed to be the same as the speed of light (3×108 m/s). An antenna is commonly used to produce electromagnetic waves. A simple type of antenna can be made from a pair of electrical conductors, one connected to each terminal of a power supply that is producing an alternating emf. The alternating emf leads to the continuous charging and discharging of the two ends of the antenna Antennas are used to start electromagnetic waves Antennas are used to start electromagnetic waves 4 4/5/2017 Antennas are used to start electromagnetic waves Radar Radar is a way of determining the distance to a faraway object by reflecting radio wave pulses off the object. Crossed, oscillating electric and magnetic fields will propagate indefinitely and without loss of energy at speed c through a vacuum. Global Positioning System The GPS receiver detects signals from at least three satellites to determine your position on the ground. Using the known positions of the satellites, the GPS unit is able to calculate your position by a process called trilateration. Hearing FM radio waves The high-frequency EM waves used by FM radio stations are known as carrier waves. FM stands for “Frequency Modulation“ AM stands for “Amplitude Modulation” The information converted into the sounds we hear is encoded as tiny variations in the frequency/amplitude of the carrier wave. Microwave cooking Water is a polar molecule and is a permanent electric dipole. Water, fat, and other substances in food absorb energy from microwaves in a process called dielectric heating. The electromagnetic spectrum The range of frequencies and wavelengths of electromagnetic waves is called the electromagnetic spectrum. A receiver decodes the variations and converts them into an electric signal that a speaker can then convert into sound. 5 4/5/2017 • Radio Waves – – – – – AM Radio Shortwave radio FM Radio Television Radar The Electromagnetic Spectrum! • Microwaves • Infrared • Visible light • Ultraviolet • X-rays • Gamma rays A mnemonic to help you remember the spectrum! (in order of increasing frequency) Radio Microwave Infrared Visible Ultraviolet X-ray Gamma Rattlesnakes May Inject Venom Upon eXtreme aGitation All of these frequencies of light travel at speed c in a vacuum (3 x 108 m/s). Human eyes are only able to detect light of wavelength 480-720 nm. That is why this is called the visible range of the spectrum. The wavelength that we perceive as red is about 480 nm. The wavelength that we perceive as violet is about 720 nm. Different animals are able to detect different ranges of EM waves! The image on the right shows the ultraviolet light given off by a dandelion. Bees and other insects have eyes that are capable of detecting UV light! The electromagnetic spectrum Why are we able to detect 480 – 720 nm electromagnetic waves with our eyes? That is the peak range of wavelengths emitted by our Sun!!! 6 4/5/2017 Mathematical description of EM waves and EM wave energy Mathematical description of EM waves The wave equation tells us: Maxwell's equations predict that the amplitudes of the changing electric and magnetic field vectors are related: Producing unpolarized light Light emitted by a lightbulb consists of many waves that originate at random times with random polarizations. If we could observe the many separate EM waves as a beam of unpolarized light moving directly toward our eyes, the oscillations of both the electric and magnetic fields would look something like a porcupine How polarized glasses work The lenses of polarized glasses are coated with a polarizing film that only transmits light whose electric field oscillates in the vertical direction. Light polarizers A polarizer absorbs one component of the E field of the EM wave passing through it, allowing the perpendicular component to pass. Brewster's law Light is traveling from medium 1 when reflects off medium 2. The reflected light is totally polarized an axis in the plane parallel to the surface when the tangent of the incident polarizing angle P equals the ratio of the indexes of refraction of the two media 𝑡𝑎𝑛𝜃𝑃 = 𝑛2 𝑛1 7 4/5/2017 Example 24.4 Polarization by scattering You are facing the Sun and looking at the light reflected off the ocean. At which angle above the horizon should the Sun be so that you get the most benefit from your polarizing sunglasses? If you look through polarized sunglasses at the clear sky in an arbitrary direction and rotate the glasses, the intensity of the light passing through the glasses changes. = 36.94 Polarization by scattering Polarization by scattering © 2014 Pearson Education, Inc. Polarization by reflection Consider light produced by the LCD screen of a calculator, cell phone, or laptop computer, or reflected off a body of water. If you look at this light through a polarizer, the intensity of reflected light varies depending on the orientation of the polarizer relative to the surfaces. This indicates that the light is partially polarized. 8 4/5/2017 Polarized LCDs Nearly all computer, TV, calculator, and cell phone screens are LCDs—liquid crystal displays. 3D movies The 3D projector produces two distinct images on the screen. Each image consists of polarized light. The two images have their polarizing axes rotated by 90° relative to each other. Polarized LCDs 1. Unpolarized light shines on the back. 2. A horizontal polarizing filter in front of the light blocks out all light waves except those vibrating horizontally. 3. Only light waves vibrating horizontally can get through. 4. A transistor switches on/off this pixel by switching on/off the electric current flowing through its liquid crystal. That makes the crystal twist. The twisted crystal rotates (or not) light waves by 90° as they travel through it. 5. Light waves that entered the liquid crystal vibrating horizontally emerge from it vibrating horizontally/vertically 6. The vertical polarizing filter in front of the liquid crystal blocks out all light waves except those vibrating vertically. The vertically vibrating light that emerged from the liquid crystal can now get through the vertical filter. 7. The pixel is lit up. A red, blue, or green filter gives the pixel its color 3D movies The film is recorded using two camera lenses sat side by side. But in the cinema, the two reels of film are projected through different polarized filters. So images destined for viewers' left eyes are polarized on a horizontal plane, whereas images destined for their right eyes are polarized on a vertical plane. Cinema goers’ glasses use the same polarizing filters to separate out the two images again, giving each eye sees a slightly different perspective and fooling the brain into 'seeing' Avatar's planet Pandora as though they were actually there. “Light is a wave” or “light behaves like a wave”? Saying that “light is a wave”, claims to know the absolute nature of light, which is not possible. Saying that “light behaves like a wave”, claims to know how to describe light, which is possible. The second statement is more accurate because it reflects the capacity of science to continually fine tune itself. Light behaves like a wave: The Wave Model of Light Light is a transverse electromagnetic wave! It is composed of perpendicular electric and magnetic fields that propagate one another. Light waves can constructively and destructively interfere with one another. Light waves obey c = 𝝀𝒇 Light waves propagate according to Huygens’ Principle. 9 4/5/2017 Frequency and wavelength of electromagnetic waves Frequency of a wave does not change upon entering a new medium! All electromagnetic waves travel at the speed of light c in a vacuum. In media other than a vacuum, the speed of electromagnetic waves is 𝒗 = Frequency is a property of the wave, and is set once the wave is produced. 𝒄 . 𝒏 Wave speed and wavelength will change inversely upon entering a new medium! The speed, frequency, and wavelength are related by 𝝀 = The frequency of an EM wave governs how much energy it carries. 𝒗 : 𝒇 Wave properties Models of Light Particle Model Reflection involves a change in direction of waves when they bounce off a barrier. Refraction of waves involves a change in the direction of waves as they pass from one medium to another. Diffraction involves a change in direction of waves as they pass through an opening or around a barrier in their path • Reflection Wave Model • Reflection • Refraction • Shadows and semishadows • Shadows and semi-shadows • Light travels in a straight line • Interference (Double slit - • Light travels in a straight line small openings) • Diffraction (Single slit - small openings) • Polarization • Doppler Effect Conceptual Whiteboard What happens to the speed and the wavelength of light as it crosses the boundary in going from air into water? Speed (A) (B) (C) (D) (E) Increases Remains the same Remains the same Decreases Decreases Wavelength Remains the same Decreases Remains the same Increases Decreases (E) 10