1. Light what is it?

2. Light what is it: moving energy particle or wave?

3. Light what is it: moving energy particle or wave? how do we decide?

4. Light what is it: moving energy particle or wave? how do we decide? if a wave, what is waving? (waving even in a vacuum?)

5. Light what is it: moving energy particle or wave? how do we decide? if a wave, what is waving: (waving even in a vacuum) Electric & Magnetic Fields

6. Properties of Light speed of light colors reflection refraction (bending) shadows energy theory absorption of light emission of light

7. Properties of Light speed of lightProperty #1 colorsProperty #2 reflectionProperty #3 refraction (bending)Property #4 shadowsProperty #5 energy theory consider in Part 4 absorption of light consider in Part 4 emission of light consider in Part 4

8. Property 1: Speed of Light particle (photon) prediction?

9. Property 1: Speed of Light particle (photon) ? no prediction wave (E&M) prediction?

10. Property 1: Speed of Light particle (photon): no prediction wave (E&M): For a wave on a string, we can start from Newton’s Second Law and get a wave equation that leads to the relation: v phase =  [T/  ] (speed of wave depends on parameters of the string the wave travels on - T is tension in the string and  is the mass density of the string)

11. Property 1: Speed of Light particle (photon): no prediction wave (E&M): Maxwell’s Eqs. In a similar way to the wave on a string, we can get a wave equation from Maxwell’s Eqs for Electromagnetism. This predicts: v phase =  [1/  o  o ] where the  o and  o are the electric and magnetic properties of vacuum.

12. Property 1: Speed of Light particle (photon): no prediction wave (E&M): Maxwell’s Eqs. in vacuum: v = [1 / {  o  o }] 1/2 where  o = 1/{4  k} = 1 / {4  * 9x10 9 Nt-m 2 /Coul 2 }  o = 4  * 1x10 -7 T-s /Coul v = [4  *9x10 9 / 4  *1x10 -7 ] 1/2 = 3 x 10 8 m/s = c units: [(Nt-m 2 /C 2 )*(C/[T-s])] 1/2 = [({kg*m/s 2 }*m 2 /C 2 )*(C/[{Nt-s/C-m}*s])] 1/2 = m/s

13. Property 1: Speed of Light particle (photon): no prediction wave (E&M): Maxwell’s Eqs. in material, v phase =  [1/  ]  = K  o, where K>1; and    o ; so v < c According to the wave theory, light should move slower in material than in vacuum.

14. Property 1: Speed of Light particle (photon): no prediction wave (E&M): in vacuum, v = c; in material, v < c we’ll come back to this when we look at refraction later in this part.

15. Property 2: Color experiment ? particle (photon) ? wave (E&M) ?

16. Property 2: Color Experiment: –invisible as well as visible –total spectrum order: radio microwave IR visible UV x-ray and gamma ray

17. Property 2: Color Experiment: –visible order: red orange yellow (yellow) green blue violet

18. Property 2: Color particle (photon): amount of energy per photon determines “color”

19. Property 2: Color particle (photon): amount of energy among different types: x-ray - most energy; radio - least in visible portion: violet - most energy; red - least

20. Property 2: Color particle (photon): amount of energy wave (E&M) ?

21. Property 2: Color particle (photon): amount of energy wave (E&M): frequency among different types of “light”: low frequency is radio (AM is 500-1500 KHz) high frequency is x-ray & gamma ray in visible spectrum: red is lowest frequency (just above IR) violet is highest frequency (just below UV)

22. Colors: frequencies & wavelengths (in vacuum) AM radio  1 MHz 100’s of m FM radio  100 MHz m’s microwave  10 GHzcm - mm Infrared (IR) 10 12 - 4x10 14 Hzmm - 700 nm visible 4x10 14 - 7.5x10 14 700nm -400nm Ultraviolet (UV) 7.5x10 14 - 10 17 400 nm - 1 nm x-ray &  ray > 10 17 Hz < 1 nm [This slide will be repeated after we see how we get these values.]

23. Property 3: Reflection particle (photon) ? wave (E&M) ?

24. Reflection particle (photon): bounces “nicely” wave (E&M): bounces “nicely” experiment: bounces “nicely” bounces nicely means: angle incident = angle reflected

25. Reflection Does a white paper reflect the light, or does a white paper emit from itself the light? - Obviously, the white paper reflects the light. Does a mirror reflect light? Of course. What is the difference between white paper and a mirror?

26. Reflection A white paper is rough on a microscopic level, and so a beam of light is reflected in all directions: A mirror is smooth on a microscopic level, and so a beam of light is all reflected in just one direction. rough paper smooth mirror Red is incoming, blue is outgoing

27. Property 4: Refraction experiment ? particle (photon)? wave (E&M) ?

28. Property 4: Refraction experiment: objects in water seem closer than they really are when viewed from air air water real object apparent location eye

29. Property 4: Refraction particle (photon) ? water air surface refracted ray incident ray

30. Property 4: Refraction particle (photon): water air surface incident ray refracted ray v xa v ya v xw v yw v xa = v xw v ya < v yw therefore v a < v w =  a =  w

31. Refraction: particle theory Since v 1x = v 2x, using the angles between the normal (the vertical) and the light rays, we have: v x1 = v x2, or v 1 sin(  1 ) = v 2 sin(  2 ), v 1 sin(  1 ) = v 2 sin(   ) (faster speed means smaller angle)

32. Property 4: Refraction wave (E&M) ? surface air water incident wave refracted wave normal line

33. Property 4: Refraction wave (E&M): surface air water incident wave refracted wave crest of wave crest of preceding wave x a w normal line crest of following wave

34. Property 4: Refraction wave (E&M):  +  = 90 o  +  = 90 o surface air water incident wave refracted wave crest of wave crest of preceding wave x a w normal line sin(  ) = a /x sin(  ) = w /x

35. Refraction: wave theory wave (E&M): Snell’s Law sin(  a ) = a /x and sin(  w ) = w /x eliminate x: a /sin(  a ) = w /sin(  w ) and use: f = v (or = v/f) to get f sin(  a ) / v a = f sin(  w ) / v w or (1/v 1 ) sin(   ) = (1/v 2 ) sin(   ) (faster speed means bigger angle) NOTE: since  a >  w, need v a > v w which agrees with wave prediction of Property 1 on speed! Note: This is opposite to the prediction of the particle theory: v 1 sin(   ) = v 2 sin(   ) with v a < v w.

36. Property 4: Refraction wave (E&M): Snell’s Law nicer form for Snell’s Law: f sin(  a ) / v a = f sin(  w ) / v w Multiply thru by c/f to get (c/v a ) sin(  a ) = (c/v w ) sin(  w ) and use definition of index of refraction: n = c/v to get n a sin(  a ) = n w sin(  w ) Snell’s Law

37. Properties 1, 2 & 4 Speed, Color and Refraction Speed of light changes in different materials Speed is related to frequency and wavelength: v = f If speed changes, does wavelength change, frequency change, or BOTH? Does color change with speed? (does color depend on frequency or wavelength?)

38. Properties 1, 2 & 4 Speed, Color and Refraction Speed of light changes in different materials Speed is related to frequency and wavelength: v = f What changes with speed: –Frequency remains constant regardless of speed –Wavelength changes with speed –Color remains constant (so color depends on frequency, not wavelength)

39. Property 4: Refraction particle (photon) theory: v w > v a wave (E&M) theory: v w < v a experiment ?

40. Property 4: Refraction particle (photon) theory: v w > v a wave (E&M) theory: v w < v a experiment: v w < v a particle theory fails! wave theory works!

41. Property 4: Refraction Snell’s Law: n a sin(  a ) = n w sin(  w ) Note that angles are measured from the normal, not the surface. Note that the index of refraction is bigger for slower speeds.

42. Property 4: Refraction Snell’s Law: n 1 sin(  1 ) = n 2 sin(  2 ) NOTE: If n 1 > n 2, THEN  1 <  2. NOTE: All  1 values between 0 & 90 degrees work fine. NOTE: Not all values of  2 work! Example: If n 1 = 1.33, n 2 = 1, and  1 = 75 o, then  2 = inv sin [n 1 sin(  1 ) / n 2 ] = inv sin [1.28] = ERROR

43. Property 4: Refraction Snell’s Law: n 1 sin(  1 ) = n 2 sin(  2 ) If n 1 sin(  1 ) / n 2 > 1 THEN there is NO value of  2 that can satisfy Snell’s law (unless you count imaginary angles!). The math is trying to tell us that there is NO transmitted ray. This is called TOTAL INTERNAL REFLECTION.

44. Property 4: Refraction The computer homework program entitled Snell’s Law (Vol. 5, #1) will give you practice in using Snell’s Law. We will now temporarily halt our look at light’s different properties, and look at some important applications of Refraction.