Download Electromagnetic Waves - Lecture Notes | PHY 184 and more Study notes Geology in PDF only on Docsity! Physics for Scientists and Engineers II Phy184, MSU Spring 1998 Lecture Notes 7 { mrt { ELECTROMAGNETIC WAVES DEFINITION OF EM-WAVES The electric and magnetic eld produced with an LC oscillator connected to an antenna in the z direction can be described with wave equations (at large distances): E = Em sin(kx !t) and B = Bm sin(kx !t). The electric and magnetic elds are always perpendicular to the direction of travel. It is a transverse wave. The electric eld is always perpendicular to the magnetic eld. The cross product ~E ~B always gives the direction of the wave. The electric and the magnetic eld are in phase and vary with the same frequency. The speed of all electromagnetic waves is given by: c = 1=p00, Em=Bm = c, c = 299; 792; 458m=s. The rate of energy transport per unit area is called the pointing vector and is given by: S = ~E ~B=0, S = E2=(c0). The intensity of the wave is de ned as I = S = E2 rms =(c0), where Erms is the root-mean-square value of the electric eld: Erms = Em= p 2. The intensity as a function of distance from the source is given by: I = Ps=(4r 2), where Ps is the power emitted by the source. The radiation pressure of a wave is de ned as Pr = I=c for total absorption and Pr = 2I=c for total re ection. POLARIZATION The electric eld component of a wave parallel to the polarizing direction of a polarizer is passed (transmitted) by the polarizer, the component perpendicular to it is absorbed. The intensity of an unpolarized wave after a polarizer is reduced by a factor of 2: I = I0=2. The intensity of a polarized wave going through a polarizer is given by I = I0 cos2 , where is the angle between the polarization direction of the wave and the polarizer. REFLECTION AND REFRACTION For electromagnetic waves re ected o surfaces the law of re ection is valid: i = r where the incident i and re ected r ray (wave) is measured with respect to the normal of the surface. For transparent materials the wave is refracted: n1 sin 1 = n2 sin 2, where n is called the index of refraction for a given material, and 1 and 2 correspond to the incoming and refracted ray, respectively. When light (em-wave) travels from an optical denser medium into an optical less dens medium all of the light is re ected at the boundary between the two media when the incoming angle is larger than a critical angle c: sin c = n2=n1,(n1 > n2). Re ected and refracted light is partially polarized. For a certain angle the re ected light is completely polarized (Brewster angle): tan B = n2=n1. 13
