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More on EM waves, Polarization Next Honor Lecture, Fri. 27 This lecture: start review on X-ray spectroscopy of proteins by Prof. P. Gilbert EM waves (Ch 34) Polarization (38.6) Normal Light without red Light without green Midterm Exam 2: Nov 1, 5:30 pm Duration 1:30 hrs, Location TBA CH 29: Magnetic fields, Motion of charged particles in B, magnetic force on a current, magnetic dipole moment and potential energy, forces between currents CH 30: Sources of magnetic fields, Biot-Savart law, field from a circular loop, solenoid, Ampere’s law and magnetic field calculations, Ampere-Maxwell’s law CH 31: Faraday’s law, Lentz’s law, Motional emf, Eddy currents, AC generators CH 34: Maxwell’s equations and their solutions, electromagnetic waves and their properties, velocity, frequency and wavelength, direction of propagation, Pointyng vector, radiation pressure 38.6: Polarization of light waves CH 35: 35.3, 35.4, 35.5: reflection and refraction of light Have clear in mind! FB = q v x B RH rule: RH rotation rule solenoid Facts on EM waves Quick Quiz pn EM waves Which orientation will have the largest induced emf? EM waves are solutions of Maxwell’s equations. E y In empty space: sinusoidal wave propagating along x with velocity E = E max cos (kx – ωt) B = B max cos (kx – ωt) • E and B are perpendicular oscillating vectors λ E·B=0 •The direction of propagation is perpendicular to E and B ExB=0 z x B loop in xz plane loop in xy plane Transverse waves 1 2 3 yz in op lo a n e pl Faraday’s law: Loops use B not E! Only the loop in the xy plane will have a magnetic flux through it as the wave passes. The flux will oscillate with time and induce an emf. 1 Quick Quiz on EM waves Quick Quiz on EM waves What is the phase difference between the sinusoidal oscillations of the electric and magnetic fields in this figure? (a) impossible to determine (b) 180° T=0 An electromagnetic wave propagates in the –y direction. The electric field at a point in space is momentarily oriented in the +x direction. The magnetic field at that point is momentarily oriented in the T/4 (a) –x direction (c) 90° (b) +y direction (d) 0 T/2 z (c) +z direction 3T/4 (d) –z direction B c y x E Quick Quiz on EM waves Relation between E and B E = Emax cos (kx – ω t) B = B max cos (kx – ωt) Sources of EM waves: oscillating charges, accelerated/decellerated charges, electron transitions between energy levels in atoms, nuclei and molecules z c E y x Intensity and Radiation pressure Energy carried by EM waves: Poynting Vector Power per unit area: rate at which energy flows through a unit area perpendicular to direction of wave propagation B Wave intensity I = time average of S over one or more cycle <cos2 (kx - ω t)> = 1/2 I ∝ E2 In a given volume, the energy is shared equally between E and B fields u E = u B since B = E/c and Total instantaneous energy density Radiation pressure: Perfectly absorbing surface P = S/c Perfectly reflecting surface P = 2S/c u =u E + uB = 1/2 ε o E2 + B 2 /(2µo ) 2 Quick Quiz on Poynting vector Quick Quiz on radiation pressure Which of the following is constant for a plane electromagnetic wave? To maximize the radiation pressure on the sails of a spacecraft using solar sailing, the sheets must be (a) magnitude of the Poynting vector (a) very black to absorb as much sunlight as possible (b) energy density uE (b) very shiny, to reflect as much sunlight as possible (c) energy density uB (d) wave intensity Which is the value of the radiation pressure in the above case? Answer: (d). The first three choices are instantaneous values and vary in time. The wave intensity is an average over a full cycle. (a) P = 2S/c Quick Quiz on EM spectrum The EM Spectrum (b) P = S/c In many kitchens, a microwave oven is used to cook food. The frequency of the microwaves is of the order of 1010 Hz. The wavelengths of these microwaves are on the order of Note the overlap between types of waves Visible light is a small portion of the spectrum Types are distinguished by frequency or wavelength (a) kilometers (b) meters (c) centimeters (d) micrometers " =c/ f = 3 #10 8 m /s = 3cm 1010 /s ! Polarization of Light Waves (38.6) plane of polarization: contains E and S Sun light is unpolarized Direction of E changes randomly Linearly polarized light: E-field has one spatial orientation Circularly polarized light: direction of E rotates with time and the tip of the vector describes a circle. Superposition of 2 waves of equal amplitude with orthogonal linear polarizations, and 90˚ out of phase. http://webphysics.davidson.edu/physlet_resources/dav_optics/Examples/polarization.html Polarization by selective absorption If linearly polarized light of intensity I0 passes through a polarizing filter with transmission axis at an angle θ along y y Polaroid sheet θ Einc = E0sinθ i + E0 cosθ j x transmission axis After the polarizer Etransm = E0cosθ j So the intensity transmitted is E0cosθ Itransm = E02 cos2θ = Ι0cos2θ Long-chain hydrocarbon molecules A polarizer is used to produce polarized light of intensity I0 and an analyzer rotated at an angle θ: transmission 100% when θ = 0 and zero when θ = 90° 3 Quick Quiz on MW demo A polarizer for microwaves can be made as a grid of parallel metal wires about a centimeter apart. The electric field vector for microwaves transmitted through this polarizer is _____ to the metal wires. Quick Quiz on Polarization (a) parallel (b) perpendicular Answer: (b). Electric field vectors parallel to the metal wires cause electrons in the metal to oscillate parallel to the wires. Thus, the energy from the waves with these electric field vectors is transferred to the metal by accelerating these electrons and is eventually transformed to internal energy through the resistance of the metal. Waves with electric-field vectors perpendicular to the metal wires pass through because they are not able to accelerate electrons in the wires. Unpolarized light (like the light from the sun) passes through a polarizing sunglass (a linear polarizer). The intensity of the light when it emerges is: Zero 1/2 1/3 1/4 I " E 2 # I " cos2 $ $ is varying randomly over fully cycle 1 Therefore, average value is 2 ! Law of Malus Example Quick Quiz on Polarization E0 TA E1 45° TA 90° unpolarized light I = I0 TA B1 I1 = 0.5 I0 I2 = I1cos2(45) I3 2) Light transmitted through first polarizer is vertically polarized. Angle between it and second polarizer is θ=45º. I2= I1 cos2 (45º)=0.5I1=0.25 I0 3) Light transmitted through second polarizer is polarized 45º from vertical. Angle between it and third polarizer is θ =45º. I3= I2 cos2(45º) =0.125 I0 Polarization by scattering When light hits a material electrons absorb and reradiate part of the light. The sky appears blue due to scattering of light on air and resulting partially polarized light. Short wavelengths (blue) are scattered more intensely than red. Optically active materials (your lab)! The light from blue sky is polarized and the direction of polarization at each point depends on the position of the Sun. They rotate the plane of polarization of incident light Solution with sugar: when polarized light passes through the Karo syrup, the direction of its polarization is changed. The rotation angle is proportional to depth and concentration of syrup. The rotation angle depends on the wavelength or color of the light. Blue light, with its shorter wavelength, rotates more than the longer-wavelength red light. Nobel prize to Frisch 1973: bees use the Sun as a compass, orienting their dance angle to the plane of polarization of the sunlight. Even when the Sun is obscured by clouds, bees can detect its position from polarization pattern of blue sky. 4