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Electromagnetic Waves

Electromagnetic Waves. Lecture 13 Electromagnetic Waves Ch. 33. Cartoon Opening Demo Topics Electromagnetic waves Traveling E/M wave - Induced electric and induced magnetic amplitudes Plane waves and spherical waves Energy transport Poynting vector Pressure produced by E/M wave

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Electromagnetic Waves

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  1. Electromagnetic Waves

  2. Lecture 13 Electromagnetic Waves Ch. 33 • Cartoon • Opening Demo • Topics • Electromagnetic waves • Traveling E/M wave - Induced electric and induced magnetic amplitudes • Plane waves and spherical waves • Energy transport Poynting vector • Pressure produced by E/M wave • Polarization • Reflection, refraction,Snell’s Law, Internal reflection • Prisms and chromatic dispersion • Polarization by reflection-Brewsters angle • Elmo • Polling

  3. Electromagnetic Waves

  4. Eye Sensitivity to Color

  5. Production of Electromagnetic waves

  6. Spherical waves Plane waves

  7. To investigate further the properties of electromagnetic waves we consider the simplest situation of a plane wave. A single wire with variable current generates propagating electric and magnetic fields with cylindrical symmetry around the wire. If we now stack several wires parallel to each other, and make this stack wide enough (and the wires very close together), we will have a (plane) wave propagating in the z direction, with E-field oriented along x, E = Ex (the current direction) and B-field along y B=By(Transverse waves)

  8. Electromagnetic Wave

  9. How the fields vary at a Point P in space as the wave goes by

  10. Electromagnetic Wave

  11. Faraday’s Law of Induction Maxwell’s Law of Induction Changing electric field induces a magnetic field Changing magnetic field induces a electric field Electromagnetic Wave Self Generation

  12. Summary

  13. Magnitude of S is like the intensity U is the energy carried by a wave

  14. Relation of intensity and power for a Spherical Wave A point source of light generates a spherical wave. Light is emitted isotropically and the intensity of it falls off as 1/r2 Let P be the power of the source in joules per sec. Then the intensity of light at a distance r is Lets look at an example

  15. (c) The power of the source is 15. The maximum electric field at a distance of 10 m from an isotropic point light source is 2.0 V/m. Calculate (a) the maximum value of the magnetic field and (b) the average intensity of the light there? (c) What is the power of the source? (a) The magnetic field amplitude of the wave is (b) The average intensity is

  16. Speed of light in Water

  17. Nothing is known to travel faster than light in a vacuum However, electrons can travel faster than light in water. And when the do the electrons emit light called Cerenkov radiation

  18. Momentum and Radiation Pressure Momentum = p What is the change in momentum of the paper over some time interval? Light beam c paper p=U/c p=0 1) Black paper absorbs all the light 2) Suppose light is 100% reflected From this we define the pressure

  19. Radiation Pressure Pr Want to relate the pressure Pr felt by the paper to the intensity of light For 100% absorption of light on the paper For 100% reflection of light

  20. Problem 21 What is the radiation pressure 1.5 m away from a 500 Watt lightbulb?

  21. Another property of light Radiation pressure: Light carries momentum This is the force per unit area felt by an object that absorbs light. (Black piece of paper)) This is the force per unit area felt by an object that reflects light backwards. (Aluminum foil)

  22. Polarization of Light • All we mean by polarization is which direction is the electric vector vibrating. • If there is no preferred direction the wave is unpolarized • If the preferred direction is vertical, then we say the wave is vertically polarized

  23. A polarizing sheet or polaroid filter is special material made up of rows of molecules that only allow light to pass when the electric vector is in one direction. Pass though a polarizing sheet aligned to pass only the y-component

  24. Unpolarized light Resolved into its y and z-components The sum of the y-components and z components are equal

  25. Intensity I0 Pass though a polarizing sheet aligned to pass only the y-component Malus’s Law One Half Rule Half the intensity out

  26. Polarizer P1 Analyzer P2 y

  27. Sunglasses are polarized vertically. Light reflected from sky is partially polarized and light reflected from car hoods is polarized in the plane of the hood Sunglass 1 Sunglass 2 Rotate sun glass 90 deg and no light gets through because cos 90 = 0

  28. 35. In the figure, initially unpolarized light is sent through three polarizing sheets whose polarizing directions make angles of 1 = 40o, 2 = 20o, and 3 = 40o with the direction of the y axis. What percentage of the light’s initial intensity is transmitted by the system? (Hint: Be careful with the angles.) Let Io be the intensity of the unpolarized light that is incident on the first polarizing sheet. The transmitted intensity of is I1 = (1/2)I0, and the direction of polarization of the transmitted light is 1 = 40o counterclockwise from the y axis in the diagram. The polarizing direction of the second sheet is 2 = 20o clockwise from the y axis, so the angle between the direction of polarization that is incident on that sheet and the the polarizing direction of the sheet is 40o + 20o = 60o. The transmitted intensity is I0 I1 I2 I3 and the direction of polarization of the transmitted light is 20o clockwise from the y axis.

  29. 35. In the figure, initially unpolarized light is sent through three polarizing sheets whose polarizing directions make angles of 1 = 40o, 2 = 20o, and 3 = 40o with the direction of the y axis. What percentage of the light’s initial intensity is transmitted by the system? (Hint: Be careful with the angles.) The polarizing direction of the third sheet is 3= 40o counterclockwise from the y axis. Consequently, the angle between the direction of polarization of the light incident on that sheet and the polarizing direction of the sheet is 20o + 40o = 60o. The transmitted intensity is Thus, 3.1% of the light’s initial intensity is transmitted.

  30. Chapter 33 Problem 34 In Figure 33-42, initially unpolarized light is sent into a system of three polarizing sheets whose polarizing directions make angles of θ1 = θ2 = θ3 = 16° with the direction of the y axis. What percentage of the initial intensity is transmitted by the system? Fig. 33-42

  31. Chapter 33 Problem 49 In Figure 33-51, a 2.00 m long vertical pole extends from the bottom of a swimming pool to a point 90.0 cm above the water. Sunlight is incident at angle θ = 55.0°. What is the length of the shadow of the pole on the level bottom of the pool? Fig. 33-51

  32. Chapter 33 Problem 62 Suppose the prism of Figure 33-55 has apex angle ϕ = 69.0° and index of refraction n = 1.59. Fig. 33-55 (a) What is the smallest angle of incidence θ for which a ray can enter the left face of the prism and exit the right face? (b) What angle of incidence θ is required for the ray to exit the prism with an identical angle θ for its refraction, as it does in Figure 33-55? In Figure 33-51, a 2.00 m long vertical pole extends from the bottom of a swimming pool to a point 90.0 cm above the water. Sunlight is incident at angle θ = 55.0°. What is the length of the shadow of the pole on the level bottom of the pool?

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