11 EM Waves Characteristics and Properties 2 Electromagnetic spectrum Gamma rays X-rays Ultraviolet Visible/Light Infrared Microwave Radio < nm > 300 ~ 10 ~ 400 ~ 700 ~ 1 ~ nm mm < 10 9 ~ 10 9 Hz 3x10 11 Hz ~ 3x10 4x Hz 8x10 ~ 4x10 14 Hz ~ 8x10 Hz 14 3x10 16 ~ 3x10 16 Hz 3x10 19 > 3x10 19 Hz Gamma rays High energetic beams: materials are transparent to it Typical energy range: in MeV or more 1MeV= 1 Million electron Volts= 1.6 x 10 Joules -13 h = 10 x 10 = 10 Joules ~ MeV ~ More particle like behaviour Sources: Nuclear transitions Rest mass of electron= m c = 0.5 MeV 2 e ~ X -rays Typical energy range: in KeV Particle like behaviour Sources: Atomic transitions (inner electrons) Characteristic X-rays Energetic electrons fired on a material target Bremsstrahlung Wavelengths of atomic dimensions or less Good probe for finding structures of substances Hard X-rays : KeV Human body is transparent : Diagnostic X-rays Characteristic X rays Ultraviolet Typical energy range: in eV Sources: Sun Atomic transitions (when electrons make long jumps ) Ozone layer in atmosphere absorbs UV from the Sun and create Ionosphere Wavelengths < 300 nm is germicidal Aquaguard 8 Ultraviolet Galaxy NASA/JPL-Caltech/SSC Visible/Light Sources: Atomic transitions (outer electrons) Hot glowing metal filament:Thermal Continuous radiation : White light Discharge through gas filled tubes: Characteristic lines: Line spectra Wave like behaviour Interference is easily shown Infrared Sources: Molecules Rotational and vibrational transitions CO 2 and H 2 O vibrational levels ~ eV Thermal radiation from human body peak around 0.01mm: many snakes sense these wavelengths Incandescent lamps radiate 50% of energy in IR region T - Rays : m (0.3 30 THz) ( 1 THz = 300 m = 4.1 meV = 33 cm -1 ) Liver cancer Star Tiger Project, Cambridge Univ. University of Delft Physikalisch-Technische Bundesanstalt Microwave Communication band extends in microwave Global System for Mobile (GSM) operates in 900/1800/1900 MHz bands Sources:Electronic ckts, Electron spin/Nuclear spin : 21cm(1.420 GHz) line of Hydrogen Useful in locating hydrogen in space CMBR: Cosmic Microwave Background Radiation 2.73 K radiation from all direction Remnant of Hot Big Bang of the past 13 Cosmic microwave background fluctuation Cosmic Background Explorer Polar molecules like water absorb EM radiations in microwave Try to align their dipole moment with the external field, setting them in rotation. Usual Microwave ovens use 12.2 cm or 2.45 GHz H H + + O - p p ~ 6.2 x 10 C-m -30 Radio Waves Radio and TV communication UHF and VHF ~ 1GHz is used for TV and FM Medium waves ~ MHz and Short waves ~ 15 MHz for radio transmission Sources: Electronic Circuits In space: Radio sources 16 Reflection and Transmission 16 17 In an inhomogeneous medium (Reflection and Transmission) 18 19 20 At the boundary x = 0 the wave must be continuous, (as there are no kinks in it). Thus we must have 21 22 We can define the transmission coefficient: (C/A) 23 We can define the Reflection coefficient: (B/A) Rigid End: 2 ( 2 >> 1 ) k 2 When 2 > 1, r < 0 Change in sign of the reflected pulse External Reflection 24 Free End: 2 0 ( 2 0 No Change in sign of the reflected pulse Internal Reflection 25 In either case: t r > 0 No Change in phase of the transmitted pulse 26 It can be seen that Stokes relations Will be also derived from Principle of Reversibility The reflectance and transmittance of Intensity is proportional to square of Amplitude 27 Huygens and Fermats Principles 27 28 Every point on a propagating wavefront serves as a source of spherical secondary wavelets, such that the wavefront at some later time is the envelope of these wavelets. Huygens Principle Huygenss Principle Every unobstructed point on a wavefront will act as a source of secondary spherical waves. The new wavefront is the surface tangent to all the secondary spherical waves. Huygenss Principle : when a part of the wave front is cut off by an obstacle, and the rest admitted through apertures, the wave on the other side is just the result of superposition of the Huygens wavelets emanating from each point of the aperture, ignoring the portions obscured by the opaque regions. 32 In optics, Fermat's principle or the principle of least time is the principle that the path taken between two points by a ray of light is the path that can be traversed in the least time. This principle is sometimes taken as the definition of a ray of light. From Fermats principle, one can derive (a)the law of reflection [the angle of incidence is equal to the angle of reflection] and (b)the law of refraction [Snells law] Fermats Principle Law of Reflection The time required for the light to traverse the path To minimize the time set the derivative to zero Law of Refraction The time required for the light to traverse the path To minimize the time set the derivative to zero 35 Principle of superposition 35 36 Principle of superposition 37 38 Resultant phasor Phasor Addition of waves Argand Diagram Representation of a complex number in terms of real and imaginary components In Complex plane A Sin t A Cos wt Re Rotating Arrow + Associated Phase Angle = Phasor Addition of two phasor Resultant Addition of three phasor 47 48 49 Problem Superposition of a large number of phasors of equal amplitude a and equal successive phase difference . Find the resultant phasor. Remember: The sum of the first n terms of a geometric series is: 50 Addition of Phasors GP series 51 52 We will revisit! 53 Coherence: Spatial, Temporal 53 54 Concept of coherence is related to stability or predictability of phase Spatial coherence describes the correlation between signals at different points in space. Temporal coherence describes the correlation between signals at different moments of time. February 16, 2008Coherence55 Figure 1: The amplitude of a single frequency wave as a function of time t (red) and a copy of the same wave delayed by (green). The coherence time of the wave is infinite since it is perfectly correlated with itself for all delays . February 16, 2008Coherence56 Figure 2: The amplitude of a wave whose phase drifts significantly in time c as a function of time t (red) and a copy of the same wave delayed by 2c(green). At any particular time t the wave can interfere perfectly with its delayed copy. But, since half the time the red and green waves are in phase and half the time out of phase, when averaged over t any interference disappears at this delay. 57 Many sinusoidal nearby frequencies are needed to construct the above Band of frequencies = Physically, monochromatic sources are fictitious. Quantifying Coherence Wave train 58 y(t) = [Sin t + Sin(1.01 t) + Sin (1.02 t) + Sin(1.03 t) + Sin (1.04 t) + Sin (1.05 t) + Sin (1.06 t) + Sin (1.07 t) + Sin (1.08 t)]/9 0 < t < 800 59 Coherence time: Coherence length: Temporal coherence: The coherence time is the time over which a propagating wave may be considered coherent. In other words, it is the time interval within which its phase is, on average, predictable. The coherence length is the coherence time times the vacuum velocity of light, and thus also characterizes the temporal (not spatial!) coherence via the propagation length (and thus propagation time) over which coherence is lost. Quantifying Coherence : Spectral width of the source in units of frequency. 60 Red Cadmium= 6438 = 10 9 Hz, 30 cm Yellow Sodium = Hz, 3 cm = 5893 He-Ne Laser= 6328 300 m = 10 6 Hz, 1. Optics Author: Eugene Hecht Class no. 535 HEC/O Central library IIT KGP