Update on the Gravitational-Wave Observatory project? Wikipedia OPL length questions: We ll go over this in lecture. Through the optics section, many

Transcription

1 More Interference

2 Update on the Gravitational-Wave Observatory project? Wikipedia OPL length questions: We ll go over this in lecture. Through the optics section, many of the equations we use don't use definitive equal signs, but approximate equal signs. Are we going to get to a point where we learn some "real" rules, or will it always be an approximation? Yes when you learn the standard model of particle physics using quantum field theory (probably not until graduate school). Actually, that model is definitely wrong, too (doesn t include gravity). Nevermind. No. We won t. I thought it was interesting to see the different colors formed in the oil films. I have always wondered why oil looked so colorful when it leaked onto the road, when it did not look so colorful otherwise. This is basically today s demonstration

3 How does electromagnetism have to do with light? Light is electromagnetic waves. That is, oscillating electric and magnetic fields. What is happening on the microscopic level when light reflects, and why does it change phase by 180 degrees? Atomic vibrations radiate reflected waves. These vibrations are out of phase.

4 Maxima: Minima How does this relate to the position on the screen? (Screen is far away)

5 intensity min max min max screen here

6 max min max min max min max screen here

7 2 PL PL d sin (approx. #1) i 1 i2 E E0 e e... I I ~ E 2 2 d 2 2 I0 cos sin dsin m dsin m L 2 I I cos dy yl(approx. #2) HW 33-4: Solve the three slit problem This only works for very narrow slits Next Lecture: wide slits

8 slits screen Three slit geometry (whiteboard/mathematica)

9 Credit: this animation and the next one are from Dr. Durfee Note: for some reason he picked the overall reference phase to be about 20

10 How many sub peaks are there between the main peaks in a 5-slit interference pattern? A. 1 B. 2 C. 3 D. 4 E. 5

11 Note: for some reason he picked the overall reference phase to be about 20-30

12 In Fig (8th edition) the textbook compares the reflection of light from a surface to the reflection of a wave on a rope. How does the analogy work? If the light is going from a smaller n to a larger n, then the phase change is 180 degrees, just like the rope who reflects of a rigid axis. This analogy is actually very helpful for me. The analogy is that from a low n to a high n light behaves like a rope reflecting off of a fixed point, while from a high n to a low n light behaves like a rope reflecting off a loose end.

13 If near perpendicular (1D Problem) For arbitrary angle (not needed for HW/exam)

14 p-polarization field amplitudes vs t r 180 phase shift (close to perpendicular) Brewster 0 phase shift (close to glancing)

15 OPL = Path Length n since wavelength inside the material is reduced by a factor of n, the distance looks bigger than it actually is Constructive interference: OPL ( any phase shifts) = m Destructive interference: OPL ( any phase shifts) = (m+1/2)

16 The concept of "optical path length" (OPL) is used in many places to analyze optical problems. (Unfortunately your textbook doesn't use it.) See for example Wikipedia, In materials with a constant index of refraction n, the OPL is just the path length times n. In the context of today's reading, why might that be a helpful concept? This is helpful in the optical interference equations. n times the path length is essentially the left hand side of those equations. The entire phenomenon of interference is dependent on a difference in phase between to identical sources of coherent light. Depending on the amount of the phase shift, varying interference patters can occur. OPL and OPD, optical path difference, provide a simple method to calculate the relative phase shift between two paths of light.

17 Discuss with your neighbor: At which surfaces is there a phase shift? Based on your answer, explain why the center is dark.

18 What does the thickness of the COATING need to be to get destructive interference between the two rays? air Rays drawn at an angle to make viewing easier. They re really perpendicular to surface. thin coating, n = 1.3 thickness t thick glass, n = 1.5