Physics 219 Question 1 Oct

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1 Lecture 13-1 Physics 19 Question 1 Oct An electromagnetic wave is traveling in +x direction and the electric field at a particular point on the x- axis points in the +z direction at a certain instant in time. At this same point and instant, what is the direction of the magnetic field? a) z b) x c) y d) +y e) None of the above

2 Lecture 13- Electromagnetic Radiation Reference: Giambattista Ch.,page Point charges at rest give rise to electric field only: E q e r A point charge moving at constant velocity gives rise to both electric and magnetic fields. Electromagnetic waves are produced only by charges that accelerate. Electromagnetic waves are also called electromagnetic radiation. ˆr A charged particle (electron) that oscillate back and forth with frequency (f) produces oscillating electric and magnetic fields at the same frequency (f). The oscillating fields travel away from the charge as EM waves. The most comment E.M. wave generator is the oscillating dipole shown next page:

3 Lecture 13-3 _1.jpg

4 Lecture 13-4 It follows from Faraday s law that electric field lines do not have to start and end on source charges. They can circulate around time varying magnetic field lines, far from the oscillating magnetic dipole. Time varying electric and magnetic fields sustain each other. However oscillating electric field without an oscillating magnetic field is impossible. A wave consisting of just an oscillating magnetic field without an oscillating electric field is also impossible. There are no electric waves or magnetic waves only electromagnetic waves.

5 Lecture 13-5 Electric Dipole Radiation k E E k Electric and Magnetic fields propagate together as a wave in an electromagnetic radiation

6 Lecture 13-6 General Properties of Wave Propagation Consider a plane water wave A It has the following properties: a.) = wavelength b.) c c.) v = velocity = c/n (compare: tsuname gulf of Mexico ) in medium of refractive index n. d.) T = period e.) A = amplitude f.) 8 31 m/s in vacuum e polarization plane v, v, v, T are related by the equations: = vt, f 1/ T

7 Lecture 13-7 E( x, t), ( x, t) The shape of the electric and magnetic wave forms are given a solutions of Maxwell differential equations and their boundary conditions. For transverse plane wave: x t sin( kx t) ez sin ( ) e T x t E Esin( kx t) ey Esin ( e T E The relation between the magnitudes points along the propagation direction E / c, E / c z z

8 Lecture 13-8 Electromagnetic Waves transverse wave! e.g. sin( ) m kx t z E E sin( ) m kx t y k E k E / c m m E / c rms E / c rms

9 Lecture 13-9 Energy Density of Electromagnetic Waves Electromagnetic waves contain energy. We know already expressions for the energy density stored in E and fields: ue 1 E Where and u defined as:, u Permittivity of free space : C /Nm 1 7 Permiability of free space : 41 Tm/A was introduced in Coulomb s law and Gauss s law. It is associated with the electric field. was introduced in Ampere s law. It is associated with the magnetic field.

10 Lecture 13-1 In 18 hundreds J.C. Maxwell starting with his Maxwell s equations i.e electric/ magnetic Gauss s Law Ampere s Law Faraday s Law derived the wave equation that describes wave propagation for any kind of wave. In case of traveling Electromagnetic wave in vacuum he found for the propagation speed: cem 1/ 8 ( ) 31 / m s When light travels through a material medium it travels with a speed v that is less than c: v c / n, where n is the index of refraction of the medium. Inserting Maxwell s results for the electromagnetic wave velocity and the -E amplitude relation into the expression for the energy density of magnetic field, we obtain:

11 Lecture E E u u E u c E So Total energy density is: rms rms u E E E u E E u E u c c c

12 Lecture 13-1 Energy Propagation in Electromagnetic Waves Energy flux density = Energy transmitted through unit time per unit area Intensity I = Average energy flux density (W/m ) P u c A I( r) P s 4 r

13 Lecture Polarization of Electromagnetic Waves Polarization is a measure of the degree to which the electric field (or the magnetic field) of an electromagnetic wave oscillates preferentially along a particular direction. linearly polarized Looking at E head-on unpolarized partially polarized components

14 Lecture Polarizer: polarization by absorption An electric field component parallel to the transmission axis is passed by a polarizer; a component perpendicular to it is absorbed. transmission axis (tourmaline, polaroid, ) So if linearly polarized beam with E is incident on a polarizer as shown, E E cos y I I cos Zero if =/, I if = If unpolarized beam is incident instead, I I cos I / Polarization can rotate in time if linearly polarized beams of different phases are combined.

15 Lecture Example: two polarizers This set of two linear polarizers produces linearly polarized light. What is the final intensity? P 1 transmits 1/ of the unpolarized light: I 1 = (1/) I P projects out the E-field component parallel to its transmission axis: E E 1 I E cos 1 I I1 cos I cos = if = / (i.e., crossed)

16 Lecture It a surface is illuminated by light intensity I, but the surface is not perpendicular to the incident light but makes an angle, the surface receives energy at a rate of: P I A I Acos A I

17 Lecture Seasonal Temperature Variation on Earth At the Earth s distance from the Sun, the radiated light intensity is: I 1 kw / m At summer solstice cos = 16.5 At winter solstice cos = 63.5 (June 1, longest day) (Dec., shortest day) P A P A Summer solstice W inter solstice I cos 11 W / m cos W / m 3 I cos 11 W / m cos W / m 3

18 Lecture _.jpg

19 Lecture Physics 19 Question Oct A beam of unpolarized light with intensity I is incident on a pair of successive polarizers as shown. The angle between the transmission axes of the polarizers is 45 degrees. What is the intensity of the outgoing light I? A..5 I..71 I C. zero D..4 I E..5 I

20 Lecture 13- specular reflection i r i r Specular and Diffuse Reflection smooth surface Object (source) at P has an image at P. Example: Road is hard to see when wet. angle of incidence = angle of reflection diffuse reflection rough surface No source is imaged. Example: wood or paper surface

21 Lecture 13-1 Plane Mirror A point object is at a distance s from a plane (or flat) mirror. The rays from the object are reflected by the mirror and the reflected rays diverge. However, the extensions of the reflected rays all intersect at a point behind the mirror, forming the image. Since no rays actually go through the image, it is called a virtual image. The image distance s is equal to the object distance s in magnitude but is opposite in sign because the image is virtual, i.e., s = - s.

22 Lecture 13- Image by Reflection from a Plane Mirror r i point object Only small fraction of reflected rays received. Virtual image at same distance from but on the other side of the mirror as the object Why? extended object An extended object can be broken into infinite number of point objects. Image has the same height and orientation as the object.

23 Lecture 13-3 Multiple Plane Mirrors equidistant depth-inversion twice at P 1 correct image!

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