1. You should have been reading Chapter 35 (interference)
this week and have started doing the first Mastering Physics assignment due on Friday !!
Please register your clicker or smart device if you have not already done so. (49/70 students).
Today’s agenda
Quiz
Intensity
Thin films
Modern Physics 2017: What is the latest LIGO rumor ?
The sub-millimeter array on Mauna Kea is a radio interferometer with 8 elements of 6 m radius, operating in the 180 GHz-418 GHz frequency range. Effective aperture is 509m. Funded by the Smithsonian Institute and the Academia Sinica.

2. Two light sources are said to be coherent if
Q1.1
Freebie !
Two light sources are said to be coherent if
Their frequencies are very close in value.
Their frequencies are the same and their relative phase does not change with time.
They are plugged into the same electrical outlet.
They have the same phase but can have different frequencies.
They can understand each other. B 2

3. Two light sources are said to be coherent if
Q1.1
Two light sources are said to be coherent if
Their frequencies are very close in value.
Their frequencies are the same and their relative phase does not change with time.
They are plugged into the same electrical outlet.
They have the same phase but can have different frequencies.
If they can understand each other. B 3

4. Two sources S1 and S2 oscillating in phase emit sinusoidal waves.
Q1.2
Two sources S1 and S2 oscillating in phase emit sinusoidal waves.
Point P is 7.3 wavelengths from source S1 and 4.3 wavelengths from source S2. As a result, at point P there is
A. constructive interference.
B. destructive interference.
C. neither constructive nor destructive interference.
D. not enough information given to decide
Answer: A

5. Q1.2
Two sources S1 and S2 oscillating in phase emit sinusoidal waves.
Point P is 7.3 wavelengths from source S1 and 4.3 wavelengths from source S2. As a result, at point P there is
A. constructive interference.
B. destructive interference.
C. neither constructive nor destructive interference.
D. not enough information given to decide
Why: = 3.0 wavelengths apart
Phase difference is an integer number of wavelengths for constructive interference; half integer for destructive interference

6. Destructive interference occurs when
Q1.3
Destructive interference occurs when
Two waves with the same frequency arriving at a location exactly half-cycle out of phase.
Two waves with the same frequency arriving at a location exactly in phase.
Two waves with the same frequency arriving at a location exactly one-cycle out of phase. A 6

7. Destructive interference occurs when
Q1.3
Destructive interference occurs when
Two waves with the same frequency arriving at a location exactly half-cycle out of phase.
Two waves with the same frequency arriving at a location exactly in phase.
Two waves with the same frequency arriving at a location exactly one-cycle out of phase. A
This is constructive 7

8. Q1.4
The interference pattern for waves emitted by two coherent sources of equal strength is shown. Which is the correct statement that describes the situation at location C?
This is a dark spot and the path difference from S1 and S2 =0.5*wavelength
This is a bright spot and the path difference from S1 and S2 =2*wavelength
This is a dark spot and the path difference from S1 and S2 =2.5*wavelength C

9. Q1.4
The interference pattern for waves emitted by two coherent sources of equal strength is shown. Which is the correct statement that describes the situation at location C?
This is a dark spot and the path difference from S1 and S2 =0.5*wavelength
This is a bright spot and the path difference from S1 and S2 =2*wavelength
This is a dark spot and the path difference from S1 and S2 =2.5*wavelength C

10. Amplitude and Intensity in Waves
Question: How are intensity and amplitude related in a wave ?
Ans: Intensity is proportional to amplitude squared i.e. I ~ A2 10

11. Amplitude and Intensity in Waves (Clicker question)
Question: An 8 foot wave is x times more intense than a 2 foot one? 4x 8x
16x
32x
Ans: Intensity is proportional to amplitude squared i.e. I ~ A2 11

12. Amplitude and Intensity in Waves
Question: An 8 foot wave is x times more intense than a 2 foot one? 4x 8x
16x
32x
82 = 64
22 = 4
16x
Ans: Intensity is proportional to amplitude squared i.e. I ~ A2 12

13. Amplitude and Intensity in Waves
Question: How are phase difference and path length difference related in a wave ?
Question: What is the meaning of ω ? How is it related to frequency ?
Question: What is the usual name for k ? 13

14. Intensity in interference patterns (Phasors)
General technique.
Result: 14

15. Intensity in interference patterns (Phasors)
Consider two interfering waves with phase different by phase angle f.
By superposition, we find the resultant wave by simply adding.
We use a phasor diagram to show the vector addition. Using the law of cosines
But so
Intensity is related to the square of the electric field through the Poynting vector
The maximum intensity is
And in terms of the maximum 15

16. Intensity in the two slit interference pattern
What is the phase difference, ϕ, at various angles θ from the slits?
Think about the path difference r2 – r1. Whenever this path difference increases by a wavelength, the phase difference increases by 2π. Thus
But the path difference for a slit separation d is just
Finally, then, the intensity pattern is
Since ,
Follow Example 35.3. 16

17. Interfering Sources 17

18. Scene from your neighborhood gas station
Thin film of oil on top of water 18

19. Interference in thin films (why so colorful ?)
Fundamentally, the interference is due to path-length differences for two coherent sources. Any arrangement that causes such a path-length difference will show interference phenomena
Figure (below) shows interference of an glass-air-glass wedge.
What is the path length difference ?
Ans: 2t
But there is a complication due to phase shifts 19

20. What is the phase shift on reflection for waves on a string ?
Will the reflected wave be inverted or not ?
Fixed end
Free end
Let’s now apply this to thin film interference 20

21. Phase shifts during reflection
Follow the analysis of thin-film interference and phase shifts during reflection.
Boundary conditions !!
How is this related to index of refraction for light ?
Ans. n = c/v
Understand the mechanical analogy !
And λ=λ0/n 21

22. Phase shifts during reflection
nb>na
na>nb
Const int
Dest. int 22

23. Thin Wedge between two plates
Suppose the two glass plates are two microscope slides 10.0 cm long. At one end they are in contact; at the other end they are separated by a piece of paper mm thick. What is the spacing of interference fringes seen by reflection ? Is the fringe at the line of contact bright or dark ? Assume monochromatic light with a wavelength in air of λ= λ0=500 nm.
What is the phase shift at each interface ?
Glass to air reflection: none
Air to Glass
reflection : (π phase shift) or λ/2
By similar triangles, t/x = h/l t=xh/l
2t =m λ0
2(xh/l) = mλ0
Condition for destructive interference 23

24. Phase shifts Example (not a clicker problem !)
nb>na
na>nb
Const int
Dest. int
A thin layer of benzene (n=1.501) lies on a top of a sheet of fluorine (n=1.434). It is illuminated from above with light whose wavelength in benzene is 400 nm.
Which of the following thicknesses of the benzene layer will maximize the reflected light ?
Ans: i) and iii)
i) 100 nm; i) 200 nm; iii) 300nm; iv) 400nm 24

25. Clicker question Hint:
Refer to the picture on the right, which reflection produces a 180o phase shift?
The first reflection.
The second reflection
Both
Neither B

26. Clicker question Hint:
Refer to the picture on the right, which reflection produces a 180o phase shift?
The first reflection.
The second reflection
Both
Neither B
n=1.3
n=1.0

27. 27

28. Do you understand why “thin films” are needed ?28

29. For next time Continue on the homework
Mastering Physics (ID on webpage)
Expected to read the book in advance
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