1. Physics 7C SS1 Lecture 4 Hitting an Interface Standing Waves Review 2D Interference

2. 2 Reaching the end of a medium Observe reflection on the wave machine… “Incident”

3. 3 Hitting an Interface Inverted Upright What happens if we send a continuous wave down the machine, it reflects, and the incoming & reflected waves interfere?

4. 4 Superposition of 2 traveling harmonic waves The period and wavelength are exactly the same. One wave travels to the right, one to the left.

5. 5 Standing Waves Fundamental

6. 6 Standing Waves 2nd Harmonic 3rd Harmonic N = “node” A = “antinode”

7. 7 Standing Waves 2nd Harmonic 3rd Harmonic What type of interference occurs at a node? a) Constructive b) Destructive c) Time-dependent d) Depends which node

8. 8 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

9. 9 Hitting an Interface Reflection and Transmission “Incident” or “Reflected”“Transmitted” “Reflected” “Transmitted”

10. 10 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.

11. 11 From spherical to planar wavefronts Planar wave front Spherical wave front

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

13. 13 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

14. 14 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

15. 15 Reflected Ray Angle of Incidence Angle of Reflection Normal Line Law of Reflection:  i =  r

16. 16 Transmitted Ray: Drive a car from a well-paved road into rough grass. Which way will it go? (a) (b)(c)

17. 17 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

18. 18 Observe the Water Compass In which medium does light travel faster? a)Air b)Water c)Same in both

19. 19 Laser Interference

20. 20 Review: 2D Interference Why is the center spot bright? a)Same frequency, same phase constant,  x=0 b)Same frequency, same phase constant,  x= c)Same frequency, phase constant and  x are both different such that  =0 d)Same frequency, phase constant and  x are both different such that  =  e)None of the above

21. 21 Review: 2D Interference Why is the 2nd dark spot dark? a)Same frequency, same phase constant,  x=0 b)Same frequency, same phase constant,  x= c)Same frequency, phase constant and  x are both different such that  =0 d)Same frequency, phase constant and  x are both different such that  =  e)None of the above  x=3 /2, in this case.)

22. 22 What is  x? a b d c e

23. 23 Review: 2D Interference Why calculate d sin  ? d sin  estimates the pathlength difference (  x). That is, how much further does the wave travel from slit 1 compared to from slit 2. When the wave splits through the slits, frequency and  don’t change, so only pathlength matters! Constructive interference occurs if one wave travels a whole number of wavelengths further than the other if  x=n  =0 or 2 , 4 , 6 , etc. Destructive interference occurs if one wave travels a half number of wavelengths further than the other if  x=(n/2)  (for n odd)  =  or 3 , 5 , 7 , etc. …so d sin  =  determines type: constructive, destructive, or partial