2. Maxwell’s Equations Differential forms electromagnetic waves y x z E ⊥ B, and E ⊥ k, B ⊥ k, k is the direction of the wave. Polarization of electromagnetic waves E and B are in phase The speed of electromagnetic wave

3. Energy Transport and the Poynting Vector The direction of the propagation of the electromagnetic wave is given by: This wave carries energy. This energy transport is defined by the Poynting vector S as: x y

4. Find the Poynting vector at point P parallel-plate capacitor of radius R. a conducting current i Example: Q O E B S Q O E B S charge increase field increase energy increase

5. (1)Find the E and B at point P (2) Find the Poynting vector at point P A conducting current i in a wire with radius R and resistivity . Example: L

6. Find the Poynting vector On wire E=0, S=0 On resistance On wireOn resistance On 

7. Example: ErEr BzBz E B

8. The Doppler effect for light 1. Sound wave, observer fixed, source moving away 2. Sound wave, source fixed, observer moving away 3. Light wave, source and observer separating

9. * o u Source or observer leaving Source or observer approaching

10. Chapter 39 Light Waves

11. Radio waves Microwaves Infrared radiation visible region Ultraviolet X raysGamma rays The sensitivity of the human eye as a function of wavelength

12. The Wavelength vs Temperature

13.  Thermal radiation—the sun light  Luminescence—cool light source    Glass ITO Matel Organic

14. The speed of light Propagation of light in matter  The speed of light in a material depends on the the frequency or wavelength.  The phase change

15. Reflection and refraction of light waves  Reflection:  Refraction: Index of refraction: n

16. rainbowIn second rainbow pattern is reversed

17. Reflection and refraction of electromagnetic waves

18. Total Internal Reflection In case of n i larger than n R

19. Examples: refraction at water/air interface Diver sees all of horizon refracted into a 97°cone. Diver ’ s illusion

20.  Optical fiber: At each contact the glass air interface, if the light hits at greater than the critical angle, it undergoes total internal reflection and stays in the fiber. Total Internal Reflection only works if n outside < n inside n inside n outside Optical fiber

21. n2n2 n1n1 d d Apparent depth: Apparent Depth 50 actual fish apparent fish B P a d’ d θ2θ2 θ1θ1 n2n2 n1n1 θ2θ2 θ1θ1

22. ACT: Refraction As we pour more water into bucket, what will happen to the number of people who can see the ball?

23. ACT: Refraction As we pour more water into bucket, what will happen to the number of people who can see the ball?

24. Huygens ’ Principle: All points on a wavefront can be considered as point sources for the production of spherical secondary wavelets. After a time t the new position of a wavefront is the surface tangent to these secondary wavelets.

25. Huygens ’ Principle: All points on a wavefront can be considered as point sources for the production of spherical secondary wavelets. After a time t the new position of a wavefront is the surface tangent to these secondary wavelets.

27. Deriving the law of refraction 11 22 n1n1 n2n2 n1  n2  v1  v2n1  n2  v1  v2  1 cannot equal  2 ! C 11 22

28. Fermat’s Principle: A B A light ray traveling from one fixes point to another fixed point follows a path such that, compared with nearby paths, the time requires is either a minimum or a maximum or remains unchange (that is, stationary). A B P d xd-x θ1θ1 ’1’1 ab

29. A B P a b d x θ1θ1 θ2θ2 n1n1 n2n2

30. Snell ’ s Law 11 11 1 2 L n1n1 n2n2 11 22 22 22 22 The two triangles above each have hypotenuse L

31. Why is the sky blue? Light from Sun scatters off of air particles–– Rayleigh scattering is wavelength-dependent, More scatter for shorter wavelengths (blue end of the visible spectrum) Less scatter for longer wavelengths (red end of the visible spectrum)

32. Sun light red and orange longer wavelengths scatter less Shorter wavelengths scatter more blue This is also why sunsets are red

33. Example

37. Exercises: P906-908 19, 36, 44 Problems P910-911 7, 12