PHYS 252 Part 1: Light

1. PHYS 252Part 1: Light what is light?

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

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

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

5. Light what is it? moving energy • wave or particle? • 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. Property 1: Speed of Light • particle (photon) ?

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

9. Property 1: Speed of Light particle (photon): no prediction wave (E&M):Maxwell’s Eqs. wave equation from Maxwell’s Eqs:

10. Property 1: Speed of Light particle (photon):no prediction wave (E&M): Maxwell’s Eqs. wave equation from Maxwell’s Eqs: is similar to the wave equation for a string: where y = y(x+/- vt) and v = [T/μ]1/2

11. Property 1: Speed of Light particle (photon): no prediction wave (E&M):Maxwell’s Eqs. wave equation from Maxwell’s Eqs predicts: E = E(x +/- vt) where

12. Property 1: Speed of Light particle (photon): no prediction wave (E&M): Maxwell’s Eqs. in vacuum: v = [1/(μoεo)]1/2 where μo = 4π x 10-6 T*m/A and εo = 1 / [4πk] = 1 / [4π x (9 x 109 Nt-m2/C2)] so v = c = [1 / {(4π x 10-7)/ (4π x 9 x 109}]1/2 m/s = [9 x 1016]1/2 m/s = 3 x 108 m/s = 670 million miles/hour

13. Property 1: Speed of Light particle (photon): no prediction wave (E&M): Maxwell’s Eqs. in material, v = [1/(με)]1/2

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 property 4 (refraction) and in Part 4 of the course when we look at Special Relativity.

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

23. Property 3: Reflection particle (photon):bounces “nicely” wave (E&M):bounces “nicely” bounces nicely means: angle incident = angle reflected

24. 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?

25. 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. Red is incoming, blue is outgoing smooth mirror rough paper

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

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

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

29. Property 4: Refraction particle (photon): incident ray vxa = vxw vxa air vya vya < vyw surface therefore va < vw vxw water vyw refracted ray

30. Refraction: particle theory Since v1x = v2x, using the angles between the normal (the vertical) and the light rays, we have: vx1 = vx2, or v1 sin(q1) = v2 sin(q2) , and we have the Pythagorean Theorem:[v2 sin(q2)]2 + [v2 cos(q2)]2 = v22 , or [v2 sin(q2)]2 = v22 - [v2 cos(q2)]2 , so if we substitute the first equation in the second, we get [v1 sin(q1)]2 = v22 - [v2 cos(q2)]2 or[v1 sin(q1)]2 = v22 [1 - cos(q2)]2 = [v2 sin(q2)]2 or v1 sin(q1) = v2 sin(q2) (faster speed means smaller angle)

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

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

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

34. Property 4: Refraction wave (E&M): 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) / va = f sin(w) / vw NOTE: since a > w, need va > vw which is opposite to the prediction of the particle theory but agrees with wave prediction of Property 1 on speed!

35. Property 4: Refraction wave (E&M): nicer form: f sin(a) / va = f sin(w) / vw Multiply thru by c/f to get (c/va) sin(a) = (c/vw) sin(w) and use definition ofindex of refraction: n = c/vto get na sin(a) = nw sin(w) Snell’s Law

36. Property 4: Refraction particle (photon) theory: vw > va wave (E&M) theory: vw < va • experiment ?

37. Property 4: Refraction particle (photon) theory: vw > va wave (E&M) theory: vw < va experiment: vw < va wave theory works! particle theory fails!

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 • If speed changes, does wavelength change, frequency change, or BOTH?

39. 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

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

41. Property 4: Refraction Snell’s Law: n1 sin(1) = n2 sin(2) • NOTE: If n1 > n2, THEN 1 < 2 . • NOTE: All 1 values between 0 & 90 degrees work fine. • NOTE: Not all values of 2 work! Example: If n1 = 1.33, n2 = 1, and 1 = 75o, then 2 = inv sin [n1 sin(1) / n2] = inv sin [1.28] = ERROR

42. Property 4: Refraction Snell’s Law: n1 sin(1) = n2 sin(2) • If n1 sin(1) / n2 > 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.

43. Property 4: Refraction • The computer homework program (entitled Snell’s Law, vol. 5, #1) will give you practice is using Snell’s Law. • We will now halt our look at light’s different properties, and look at some important applications of Refraction for the rest of Part 1. We will continue looking at other properties in Part 2 of the course.