= W m 2. = J = 7.50 MeV

Transcription

1 Phyic 111 Fall 7 Light Solution 1 The huan eye i ot enitive to light having a wavelength of 55 7, which i in the green yellow region of the viible electroagnetic pectru What i the frequency of thi light? 14 1 The frequency i given fro c = fλ f = = = 55 7 λ 55 A diathery achine, ued in phyiotherapy, generate electroagnetic radiation that give the effect of deep heat when aborbed in tiue One aigned frequency for diathery i 733 MHz What i the wavelength of thi radiation? The wavelength i given fro c fλ λ = = = f 733 = 3 A neodyiu yttriu aluinu garnet laer ued in eye urgery eit a 3-J pule in n, focued to a pot 3 µ in diaeter on the retina (a) Find (in SI unit) the power per unit area at the retina (Thi quantity i called the irradiance in the optic indutry) What energy i delivered to an area of olecular ize, taken a a circular area 6 n in diaeter? (a) I = ( 3 3 J) 9 ( ) π( 15 6 ) = W ( ) = 1 J = 75 MeV ( ) ( 3 3 J) A handheld cellular telephone operate in the 86- to 9-MHz band and ha a power output of 6 W fro an antenna c long (a) Find the average agnitude of the Poynting vector 4 c fro the antenna, at the location of a typical peron head Aue that the antenna eit energy with cylindrical wave front (The actual radiation fro antenna follow a ore coplicated pattern) The ANSI/IEEE C axiu expoure tandard i 57 W/c for peron living near cellular telephone bae tation, who would be continuouly expoed to the radiation Copare the anwer to part (a) with thi tandard

2 The area over which we odel the antenna a radiating i the lateral urface of a cylinder, A = π rl = π ( 4 ) ( )= 51 (a) The intenity i then: S = P A = 6 W 51 = 39 W The tandard i: 57 W c = 57 W c ( ) 3 W W 4 c = 57 W While it i on, the telephone i over the tandard by 39 W = 419 tie 57 W 5 A plane electroagnetic wave i traveling along the x-axi If the electric field of the wave ha a axiu value of x -4 N/C and lie along the y-axi, find the wave' axiu agnetic field and it direction 4 N E C 13 The agnetic field i given by E = cb B = = = 667 T in the z- direction 6 Unpolarized light of intenity I o pae through a Polaroid with it traniion axi vertically oriented What intenity eerge? If the tranitted light pae through a econd Polaroid heet with it traniion axi 6 o to the vertical what fraction of the original incident light intenity I o eerge? Through the 1 t polarizer, ½ of the original intenity eerge Thi vertically polarized light i then incident on a nd polarizer oriented at 6 o to the vertical The intenity that eerge So i S = co 6 = 15So = 15% So

3 7 Three polarizer arranged in erie are each oriented at 3 o fro the previou one If an unpolarized light bea travel through the three polarizer and eerge with an intenity of W/, what wa the intenity of the bea incident on the firt polarizer? Through the 1 t polarizer, ½ of the original intenity eerge, or S 1 = Through the S o econd polarizer, the intenity that eerge i S = S1 co 3 = co 3 = 375S o Thi light i incident on a 3 rd polarizer and the intenity that eerge i S3 = S co 3 = 375S o co 3 = 81S o It i found that the actual intenity that eerge i W/ W W Thu the initial intenity i = 81S S = 71 S o 8 Suppoe a 5-kW radio tation eit EM wave uniforly in all direction (a) How uch energy per econd croe a - area fro the tranitting antenna? What i the r agnitude of the E r field at thi point, auing the tation i operating at full power? (c) What i the voltage induced in a --long vertical car antenna at thi ditance? (a) The radio wave have the ae intenity in all direction, o the energy per unit area per unit tie over a phere centered at the ource with a radiu of i S = P A = P 5 3 W = 4π r 4π ( ) = 398 W ( ) Thu the power through the area i P = SA = 398 W ( )= 4 W We find the r value of the electric field fro S = cε E r ; 398 W = ( 3 )885 ( 1 C N )E r, which give E r = 1 V (c) The voltage over the length of the antenna i E r = V r = E r d = ( 1 V ) ( )= 1 V

4 9 Repeat proble #8 for a ditance of k fro the tation (a) The radio wave have the ae intenity in all direction, o the energy per unit area per unit tie over a phere centered at the ource with a radiu of k i S = P A = P 5 3 W 4πr = 4π 3 Thu the power through the area i P = SA = W ( ) ( ) = W We find the r value of the electric field fro ( )= W = 4 µw S = cε E r ; W = ( 3 )885 ( 1 C N )E r, which give E r = 1 V (c) The voltage over the length of the antenna i E r = V r = E r d = ( 1 V ) ( )= 1 V What i the axiu power level of the radio tation of Proble #8 o a to avoid electrical breakdown of air at a ditance of fro the antenna? Aue the 6 antenna i a point ource Air break down in an electric field of about 3 V The energy per unit area per unit tie i S = 1 cε E ; = 1 3 ( )885 ( 1 C N )3 ( 6 V) = W The power output i P = S 4π r = W 4π ( ) = W An EM wave ha frequency 966 Hz What i it wavelength, and how would we claify it? The wavelength i given fro 7 c = fλ λ = = = 313 = 313n which i in the ultraviolet 14 1 f 966 portion of the EM pectru

5 1 Our nearet tar (other than the Sun) i 4 light-year away That i, it take 4 year for the light it eit to reach Earth How far away i it in eter? A light year i the ditance that light travel in one year Since the nearet tar (Proxia Centari) i 4 light-year away, the light ha to travel a ditance equal to 7 d c = d = ct = 3 4yr = 398 t 1yr