Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Lecture 22: July 15th 2009 Physics for Scientists and Engineers II Physics for Scientists and Engineers II , Summer Semester 2009 1 Momentum and Radiation Pressure Electromag netic radiation carries energy TER and momentum p per unit time. If TER is totally absorbed by a surface perpendicu lar to S, the momentum p transporte d to the surface has a magnitude : T p ER (complete absorption ) c A pressure P is exerted on the surface by the radiation (" radiation pressure" ) dTER dt Savg I F 1 dp 1 d TER 1 P (complete absorption ) A A dt A dt c c A c c (Note : P here is pressure, not power) 2Savg 2I 2T For complete reflection : p ER and P c c c Physics for Scientists and Engineers II , Summer Semester 2009 2 Antennas Stationary charges : Produce constant electric fields Constant currents : Produce constant magnetic fields Maxwell' s equations tell us that we need time - varying fields to produce electromag netic radiation. Accelerate d charges needed to produce time - varying fields. Whenever a charged particle accelerate s, it radiates energy (em radiation) . 4 + + The Half Wave Antenna + + Source of alternating voltage having frequency f = c / Conducting rods 4 - - Physics for Scientists and Engineers II , Summer Semester 2009 3 Driving the resonance frequency of the antenna ----??? You can create a driven oscillatio n by applying an alternatin g voltage with c a frequency equal to the self - oscillatio n frequency of the antenna (f ). 2L Resonance occurs with higher amplitudes (greater electric fields, greater current). Snapshot in time: + + + S B I E I + - B S Separation of charges creates an electric field like that of a dipole: Given the name “Dipole antenna” E - - B E at all points in space and time. Physics for Scientists and Engineers II , Summer Semester 2009 4 Driving the resonance frequency of the antenna + + Snapshot in time: + S B I + B S (indicatin g the direction E I - E in which energy flows) - B E at all points in space and time. E and B are 90 out of phase (e.g., when I 0, the charges at the outer ends of the rods are at a maximum). Physics for Scientists and Engineers II , Summer Semester 2009 5 Voltage and Current Distribution V I V I V I V I Physics for Scientists and Engineers II , Summer Semester 2009 6 Driving the resonance frequency of the antenna V I Physics for Scientists and Engineers II , Summer Semester 2009 7 The “near field” (dipole field) behavior + + + + + + S B I E I + - B S B I S E I E - + - B E - - Shortly th ereafter, the current reverses : Poynting vector reverses direction Energy flowing inward no net flow of energy ??? No! The dipole field (near field) falls of proportion al to 1 and quickly becomes insignific ant. 3 r Physics for Scientists and Engineers II , Summer Semester 2009 8 The “far field” behavior At larger distances time - varying electric fields induce time varying magnetic field and vice versa according to E ds d B dt Faraday' s law d E Ampere - Maxwell law dt The magnetic and electric fields produced in this manner are in phase. 1 E and B are proportion al to r 1 radiation looses intensity proportion al to 2 r B d s 0 I I d 0 I 0 0 Physics for Scientists and Engineers II , Summer Semester 2009 9 Angular dependence of radiation intensity S Intensity of Radiation : I S avg sin 2 r2 Similarly, when using an antenna to receive radiation, orientatio n matters equally. S Physics for Scientists and Engineers II , Summer Semester 2009 10 Angular dependence of radiation intensity Similarly, when using an antenna to receive radiation, orientatio n matters equally. E S B Sender Good reception S Sender No reception S B Sender No reception E E should be parallel to antenna Physics for Scientists and Engineers II , Summer Semester 2009 11 Electromagnetic Spectrum Physics for Scientists and Engineers II , Summer Semester 2009 12 The Nature of Light Newton: Light = Stream of Particles (can explain reflection and refraction) 1678 Christian Huygens : Showed that a wave model of light can also explain reflection and refraction. 1801 Thomas Young: Experimental demonstration of the wave nature of light (Double slit experiment “Interference” effects) Maxwell: Light = high frequency electromagnetic wave Hertz: Confirms existence of electromagnetic waves …..but also discovers the photoelectric effect (contradicts the wave model, which predicts: more light intensity = more energy transferred to electrons) Einstein 1905: Proposes that energy of light wave is present in particles called photons. E=hf is the energy of a photon (explains photoelectric effect). Physics for Scientists and Engineers II , Summer Semester 2009 13 Measuring the speed of light Galileo: Using lanterns between mountains didn’t work. The light is too fast. 1675: Ole Roemer found that the period of revolution of the moon Io around Jupiter depends on whether the earth is receding from or moving towards Jupiter (longer period when earth is receding). From these data Huygens calculated c > 2.3 x 108 m/s 1849: Fizeau’s method (toothed wheel): c = 3.1 x 108 m/s Currently accepted value: c = 2.997 9 x 108 m/s Physics for Scientists and Engineers II , Summer Semester 2009 14 Eclipse Time Delay of Io in the shadow of Jupiter Roemer’s method Jupiter Io being eclipsed by Jupiter 2 Rsunearth c tdelay Sun In this position, the time of the eclipse is delayed by many minutes compared to the opposite position of the earth. Physics for Scientists and Engineers II , Summer Semester 2009 15 Ray Approximation in Geometric Optics Geometrical Optics The study of the propagation of light under these assumptions: 1) In a uniform medium light travels in a straight line. 2) Light changes direction in a medium with non-uniform optical properties, or at the interface between two media. The “Ray approximation”: Wave moving through a medium travels in a straight line in the direction of it’s rays. Rays Physics for Scientists and Engineers II , Summer Semester 2009 Wave fronts 16 Ray Approximation in Geometric Optics Encountering barriers (like an opening in a wall): The ray approximation is valid if << d, where d is the size of the opening. d Wave continues in a straight line d Diffraction occurs Opening acts like a point source of a wave. Physics for Scientists and Engineers II , Summer Semester 2009 17 Reflection of Light/Wave Incident Ray Normal 1 Reflected Ray 1' 1' 1 Angle of reflection Angle of incidence Physics for Scientists and Engineers II , Summer Semester 2009 18 Specular and Diffuse Reflection Specular reflection “Smooth surface” Variations in surface Diffuse reflection Physics for Scientists and Engineers II , Summer Semester 2009 19 The Wave under Refraction Incident Ray Normal 1 2 1' v1 Air Glass v2 v1 2 Angle of Refraction Physics for Scientists and Engineers II , Summer Semester 2009 Reflected Ray Refracted Ray 20 The Wave under Refraction Incident Ray, Reflected Ray, and Refracted ray are all in one plane. sin 2 v2 Speed of light in medium 2 sin 1 v1 Speed of light in medium 1 Physics for Scientists and Engineers II , Summer Semester 2009 21 The Wave under Refraction Incident Ray Normal 1 Reflected Ray 1' v1 Glass Air v2 v1 2 1 Angle of Refraction Physics for Scientists and Engineers II , Summer Semester 2009 Refracted Ray 22 Index of Refraction – not yet covered in class but needed for HW 16 Index of Refraction : n speed of light in vacuum c speed of light in a medium v n vacuum 1 For vacuum : All other media : n 1 When light enters a medium : frequency remains constant, but wavele ngth changes. f1 f 2 f v1 1 f v2 2 f v1 c 1 v n1 n2 f 1 v c 2 v2 n1 2 f n n 1n1 2 n2 n2 Wavelength in vacuum n Wavelength in medium Physics for Scientists and Engineers II , Summer Semester 2009 23 Snell’s Law of Refraction – not yet covered in class but needed for HW 16. sin 2 v2 n1 sin 1 v1 n 2 n1 sin 1 n 2 sin 2 Snell’s Law of Refraction Physics for Scientists and Engineers II , Summer Semester 2009 24