1. 1 Physics 7C SS1, Lecture 5: Wave and Ray Models Standing waves Reflection/Refraction Optics

2. 2 Agenda Determine content students want lecture about Discuss any review material about interference (including beats and standing waves) Develop any current material about the ray model (reflection and refraction) Introduce any new material about the ray model (optics)

3. 3 What should lecture cover? (1st choice) Review of aspects of the wave model 1)Multiple-slit interference 2)Beats 3)Standing Waves Move forward with the ray model 4)Reflection and refraction 5)Next material: lenses

4. 4 What should lecture cover? (2nd choice) Review of aspects of the wave model nMultiple-slit interference 1)Beats 2)Standing Waves Move forward with the ray model 4)Reflection and refraction 5)Next material: lenses

5. 5 Interference Fundamentals  = -4 , -2 , 0, +2  … is constructive  = -3 , - , +  … is destructive  =anything else…is partial 2π  2π  Unit circle Wave 1 Wave 2 Difference

6. 6 Interference for differing frequencies: Beats 12345 What type of interference occurs at each point?

7. 7 Interference for differing frequencies: Beats 12345

8. 8 12345 The carrier frequency The beat frequency

9. 9 Standing Waves Fundamental

10. 10 Standing Waves 2nd Harmonic 3rd Harmonic N = “node” A = “antinode”

11. 11 Standing Waves 2nd Harmonic 3rd Harmonic What type of interference occurs at an antinode? a)Constructive b)Destructive c)Time-dependent d)Depends which antinode

12. 12 Testing Standing Waves When the wave looks like this: the frequency is 45Hz. What is the lowest possible frequency? a)9 Hz b)12.5 Hz c)15 Hz d)30 Hz e)135 Hz f)Other

13. 13 Testing Standing Waves When the wave looks like this: the frequency is 45 Hz. What is the highest possible frequency? a)9 Hz b)12.5 Hz c)15 Hz d)30 Hz e)135 Hz f)Other

14. 14 Testing Standing Waves The figure below is for node-node waves. Draw the same harmonic for antinode-node waves. If this frequency is 45 Hz. What is the lowest possible frequency? (enter a numeric response rounded to the nearest whole number, no decimal places)

15. 15 Testing Standing Waves The figure below is for node-node waves. Draw the same harmonic for antinode-node waves. If this frequency is 45 Hz. What is the lowest possible frequency? (enter a numeric response rounded to the nearest whole number, no decimal places) a)9 Hz b)12.5 Hz c)15 Hz d)30 Hz e)135 Hz f)Other

16. 16 Wavefronts and Rays A wavefront represent points of equal phase (e.g. the crest of the wave). The ray shows the direction in which the wavefront is moving. Rays are perpendicular to wavefronts.

17. 17 From spherical to planar wavefronts Planar wave front Spherical wave front

18. 18 Identify the representation: 12 (a)Both wavefront (b)Both ray (c)1 is wavefront, 2 is ray (d)1 is ray, 2 is wavefront

19. 19 What (typically) happens next? 12 (a)There is a reflected wave (b)There is a transmitted wave (c)Both reflected and transmitted waves (d)Neither reflected nor transmitted waves

20. 20 Transmitted Ray: Drive a car from a well-paved road into rough grass. Which way will it go? (a) (b)(c)

21. 21 Transmitted Ray: Transmitted ray is bent, or “refracted” Angle of Incidence Angle of Refraction Law of Refraction or “Snell’s Law:” n 1 sin  1 =n 2 sin  2 n : “index or refraction” speed of light in vacuum speed of light in material

22. 22 Reflected Ray Throw a ball at a wall, view from above. Which is the correct path, assuming a perfectly elastic collision? (a)(b)(c) (d) Depends

23. 23 Reflected Ray Angle of Incidence Angle of Reflection Normal Line Law of Reflection:  i =  r

24. 24 Reflected Wavefronts Angle of Incidence Angle of Reflection Normal Line Law of Reflection:  i =  r

25. 25 Observe the Water Compass In which medium does light travel faster? a) Air b) Water c) Same in both What happens if the angle in the water gets increasingly large?

26. 26 Observe on the Optics Board What are you seeing? Reflection Refraction Total Internal Reflection Convergence Divergence

27. 27 Light at an Interface (Activity 8.6.3 & FNT 1) Incoming Ray Plastic prism n = 1.5 On entering the prism (first boundary), which way will the light bend? a) Upb) Downc) No bend Air n = 1

28. 28 Light at an Interface Incoming Ray Plastic prism n = 1.5 Which Ray? (a) (b) (c) Air n = 1

29. 29 Parallel rays are uncommon… how do lenses work on regular objects?

30. 30 What do we see?

31. 31 Every part of the tree reflects light, scattering it all directions. A ray diagram is used to simplify this picture.