Electromagnetic Waves

Transcription

1 EM Waves aroud Electromagetic Waves Chapter 3 Eergy from the Su EM waves Light EM waves Galaxy M04 (see

2 Galaxies/NGC History - Maxwell s Theory I 865, James Clerk Maxwell developed a theory about electricity ad magetism. His startig poits were:. Electric field lies origiate o + charges ad termiate o charges.. Magetic field lies form closed loops. 3. A time varyig magetic field iduces a electric field 4. A magetic field is created by a curret. Charges ad Fields, Summary Statioary charges produce oly electric fields Charges i uiform motio (costat velocity) produce electric ad magetic fields Charges that are accelerated produce electric ad magetic fields ad electromagetic waves Maxwell s theory is a mathematical formulatio that relates electric ad magetic pheomea. His theory, amog other thigs, predicted that electric ad magetic fields ca travel through space as waves ad he was able to predict the speed of travel. The uitig of electricity ad magetism resulted i the Theory of Electromagetism. Electromagetic Waves, Summary A chagig magetic field produces a electric field A chagig electric field produces a magetic field These fields are i phase At ay poit, both fields reach their maximum value at the same time Maxwell s Predictios A time depedet electric field produces a magetic field ad visa versa. Acceleratig charges will radiate electromagetic waves. Electromagetic waves travel at the speed of light c: 8 c = m / s The electric ad magetic fields i the wave are fluctuatig i both space ad time.

3 EM Waves ad Hertz I 887, Heirich Hertz geerated ad detected electromagetic waves i his lab. The waves radiated from a trasmitter circuit ad were detected i a receiver circuit. Hertz used the fact that electrical circuits have resoat frequecies just like mechaical systems do. Producig EM Waves Electromagetic waves will be produced whe a charge udergoes acceleratio. If a ac voltage is applied to a atea, the charges will be accelerated up ad dow ad radiate EM waves. The radiated waves are made up of electric ad magetic fields. A travelig electromagetic wave produced by a ac geerator attached to a atea. A travelig electromagetic wave produced by a ac geerator attached to a atea. At t = 0 the electric field at poit P is dowward. After oe quarter of a cycle, at t = /4 T, the electric field at P vaishes. A short time later the electric field at P is still dowward, but ow with a reduced magitude. Note that the field created at t = 0 has moved to poit Q. The decreasig electric field at poit P creates a magetic field at poit Q poitig ito the viewgraph The charge o the atea has reversed polarity ow, ad the electric field at P poits upward. Whe the oscillator has completed half a cycle, t = / T, the field at poit P is upward ad of maximum magitude. At t = 3/4 T the field at P vaishes agai. The fields produced at earlier times cotiue to move away from the atea. Field directios i a electromagetic wave Computer Simulatio At a time whe the electric field produced by the atea poits dowward, the magetic field poits ito the page. I geeral, the electric ad magetic fields i a electromagetic wave are always at right agles to each other. A electromagetic wave propagatig i the positive x directio. Note that E ad B are perpedicular to each other ad i phase. The directio of propagatio is give by the thumb of the right had, after poitig the figers i the directio of E ad curlig them toward B (palm towards B). 3

4 Properties of EM Waves The radiated EM waves have certai properties: EM waves all travel at the speed of light c. c = /(e 0 μ 0 ) the E ad B fields are perpedicular to each other the E ad B fields are i phase (both reach a maximum ad miimum at the same time) for EM waves i vacuum E=cB The E ad B fields are perpedicular to the directio of travel (trasverse waves) Receivig radio waves Basic elemets of a tuig circuit used to receive radio waves. First, a icomig wave sets up a alteratig curret i the atea. Next, the resoace frequecy of the LC circuit is adjusted to match the frequecy of the radio wave, resultig i a relatively large curret i the circuit. This curret is the fed ito a amplifier to further icrease the sigal. Electromagetic radiatio is greatest whe charges accelerate at right agles to the lie of sight. Zero radiatio is observed whe the charges accelerate alog the lie of sight. These observatios apply to electromagetic waves of all frequecies. Plae Waves EM waves i free space are plae waves. That meas that the E ad B fields are cofied to a plae ad uiform withi the plae at all time. As we said, EM waves travel at the speed of light. Light speed ca be derived from two other quatities we have already used: c = 8 = 3 0 μ ε 0 0 m/s Light Light is a electromagetic wave c = fλ = 3 0 λ f wavelegth frequecy m/s As light waves travel through space they: trasport eergy trasport mometum 8 Light from Su about 8 miutes Light from stars years! EM waves ca be geerated i differet frequecy bads: radio, microwave, ifrared, visible, ultraviolet, x-rays, gamma rays Notes o The EM Spectrum Note that the visible portio of the spectrum is relatively arrow. The boudaries betwee various bads of the spectrum are ot sharp, but istead are somewhat arbitrary. ( m = 0-9 m Radio Waves Used i radio ad televisio commuicatio systems Microwaves Wavelegths from about mm to 30 cm Well suited for radar systems Microwave oves are a applicatio 4

5 Notes o the EM Spectrum, Ifrared waves Icorrectly called heat waves Produced by hot objects ad molecules Readily absorbed by most materials Visible light Part of the spectrum detected by the huma eye Most sesitive at about 560 m (yellow-gree) Notes o the EM Spectrum, 3 Ultraviolet light Covers about 400 m to 0.6 m Su is a importat source of uv light Most uv light from the su is absorbed i the stratosphere by ozoe X-rays Most commo source is acceleratio of high-eergy electros strikig a metal target Used as a diagostic tool i medicie Notes o the EM Spectrum, fial Gamma rays Emitted by radioactive uclei Highly peetratig ad cause serious damage whe absorbed by livig tissue Lookig at objects i differet portios of the spectrum ca produce differet iformatio Problem Fid the frequecy of blue light with a wavelegth of 470 m. c = λ f 8 c 3 0 f = = λ = 9 Problem Hz As you drive by a AM radio statio, you otice a sig sayig that its atea is 4 m high. If this height represets oe quarter-wavelegth of its sigal, what is the frequecy of the statio? λ 4 m = therefore λ = 4 4 = 568 m 4 8 c 3 0 f = = = 58 khz λ 568 Doppler Effect ad EM Waves A Doppler Effect occurs for em waves, but differs from that of soud waves For soud waves, motio relative to a medium is most importat For light waves, the medium plays o role sice the light waves do ot require a medium for propagatio The speed of soud depeds o its frame of referece The speed of em waves is the same i all coordiate systems that are at rest or movig with a costat velocity with respect to each other Doppler Equatio for EM Waves The Doppler effect for em waves u f0 fs ± c f o is the observed frequecy f s is the frequecy emitted by the source u is the relative speed betwee the source ad the observer The equatio is valid oly whe u is much smaller tha c 5

6 Doppler Equatio, cot The positive sig is used whe the object ad source are movig toward each other The egative sig is used whe the object ad source are movig away from each other Astroomers refer to a red shift whe objects are movig away from the earth sice the wavelegths are shifted toward the red ed of the spectrum examples: Nexrad (The Doppler weather radar) NAVSTAR Navigatio system Eergy ad Mometum i EM Waves The EM waves carry eergy The eergy desity u (eergy per uit volume) i a regio of empty space where electric ad magetic fields are preset is u = ε 0E + B = ε0e = B μ0 μ0 The average power per uit area i a EM wave is also called itesity of the wave (I = power/area: uits W/m ) ε0 I = Emax = ε0cemax μ0 Radiatio Pressure The EM waves carry eergy ad mometum p For a electromagetic wave absorbed by a area A the average mometum trasferred to the surface is IAΔt This mometum trasfer is resposible Δp = c for the pheomeo of radiatio pressure. Whe a EM wave is completely absorbed by a surface perpedicular to the directio of propagatio of the wave, the rate of chage of mometum equals the force o the surface (uits Pa = N/m. pressure = force/area). I For a totally reflective I pressure = pressure = c surface c Questio If a light beam carries mometum, should a perso holdig a flashlight feel a recoil aalogous to the recoil of a rifle whe it is fired?? Questio? Why is the radiatio pressure o a perfectly reflectig surface twice as great as o a perfectly absorbig surface? The reflectio of light 6

7 Reflectio ad Refractio Whe a light ray travels from oe medium to aother, part of the icidet light is reflected ad part of the light is trasmitted at the boudary betwee the two media. The trasmitted part is said to be refracted i the secod medium. icidet ray reflected ray refracted ray Types of Reflectio If the surface from which the light is reflected is smooth, the the light udergoes specular reflectio (parallel rays will all be reflected i the same directios). If, o the other had, the surface is rough, the the light will udergo diffuse reflectio (parallel rays will be reflected i a variety of directios) The Law of Reflectio For specular reflectio the icidet agle θ i equals the reflected agle θ r : θ i = θ r The Refractio of Light The agles are measured relative to the ormal as show. The Refractio of Light The speed of light is differet i differet materials. We defie the idex of refractio,, of a material to be the ratio of the speed of light i vacuum to the speed of light i the material: c = v Whe light travels from oe medium to aother its velocity ad wavelegth chage, but its frequecy remais costat. For a vacuum, = For other media, > is a uitless ratio Sell s Law I geeral, whe light eters a ew material its directio will chage. The agle of refractio θ is related to the agle of icidece θ by Sell s Law: siθ siθ = v v where v is the velocity of light i the medium. Normal lie Sell s Law ca also be writte as θ = siθ si θ The agles θ ad θ are measured relative to the lie ormal to the surface betwee the two materials. Air Glass θ 7

8 Example: Which way will the rays bed? Applicatio Day ad Night Settigs o Auto Mirrors =.4 = =.6 =. Which of these rays ca be the refracted ray? = siθ si θ With the daytime settig, the bright beam of reflected light is directed ito the driver s eyes With the ighttime settig, the dim beam of reflected light is directed ito the driver s eyes, while the bright beam goes elsewhere A Commo Mirage Problem problem You have a semicircular disk of glass with a idex of refractio of =.5. Fid the icidet agle θ for which the beam of light i the figure will hit the idicated poit o the scree. siθ = siθ 5 siθ =.5 siθ taθ = 0 o Therefore θ = 4 siθ =.5 si4 Therefore θ =.6 o o problem Total Iteral Reflectio Whe light travels from a medium with >, there is a agle, called the critical agle θ c, at which all the light is reflected ad oe is trasmitted. This process is kow as total iteral reflectio. The icidet ray is both reflected ad refracted. Total Iteral Reflectio 8

9 A particular agle of icidece will result i a agle of refractio of 90 This agle of icidece is called the critical agle siθ c = for > Critical Agle A applicatio of iteral reflectio Plastic or glass rods are used to pipe light from oe place to aother Applicatios iclude medical use of fiber optic cables for diagosis ad correctio of medical problems Telecommuicatios Fiber Optics Problem problem A ray of light eters the log side of a prism ad udergoes two total iteral reflectios, as idicated i the figure. The result is a reversal i the ray s directio of propagatio. Fid the miimum value of the prism s idex of refractio,, for these iteral reflectios to be total. At the first reflectio, med o si 45 = This is the same for the secod reflectio. Therefore, o si 45 med med med = o si 45 =.44 or problem Questio? Questio? Sometimes whe lookig at a widow, oe sees two reflected images, slightly displaced from each other. What causes this effect? A studet claims that, because of atmospheric refractio, the su ca be see after it has set ad that the day is therefore loger tha it would be if the earth had o atmosphere. What does the studet mea by sayig the su ca be see after it has set? Does the same effect also occur at surise? 9

10 Dispersio The idex of refractio of a material depeds o wavelegth! It is called dispersio. Example: Polarizatio Polarized ad upolarized light Polarizatio by filters by reflectio 0