1. Physics 11 Advanced Mr. Jean May 29 th, 2012

2. The plan: Video Clip of the day Modern Physics –Relative motion –Light is a problem Einstein’s change to thinking Time Dilation

3. Thin Film Interference: Thin Film Interference: This occurs when light travels through a very thin layer of transparent material. Thin film interference occurs with oil films, soap bubbles, etc. Light that is incident on the film has several things happen to it. –Some of the light is reflected off the top of the film. These waves have a 180  phase change since the index of refraction for the film is greater than for air. –Next, the light that goes into the film is refracted as it travels from air into the film. Some of the light goes into the air on the other side of the film. This light is refracted (back the other way). –Finally, some of the light is reflected off the air/film surface. This light does not undergo any phase change.

4. The film has a thickness of t. We let n be the index of refraction for the film. The index of refraction for air is, of course, 1. Ray 1 reflecting off the surface of the film has a 180  phase change. Ray 2 reflecting off the opposite film surface has no phase change. The two rays are out of phase.

5. Thin Film Problems: The two waves will recombine when you look into the film and the rays enter your eyes. If the path difference is half of the wavelength, or an odd multiple of the wavelength, then the waves will end up in phase and you will see constructive interference – a bright fringe. The basic kind of problem involves finding the minimum thickness that will cause constructive or destructive interference. This minimum would be when the wave came straight down onto the film. This means that the angle of incidence is zero.

6. We can solve for the wavelength in the film! We start with the equation for the index of refraction.

7. We’ll call the wavelength in the film f. This means that the minimum thickness is given by:

8. Example:

9. Relative Motion: In order to understand Albert Einstein's "Theory of Relativity", one must first understand the concept of relative motion. In the diagram following, the velocities of objects are relative to some other object.

11. Worst Husband ever award: Last year I travelled to Singapore. It was an incredible experience; more importantly I threw an object quicker than I will ever throw again. Somewhere between NYC and Munich, Germany at 30,000 feet in the air we were traveling nearly 850km/h. I decided to throw a piece of paper at my wife.

12. Worst Husband ever award: Let’s say I only threw the ball of paper at 40km/h. Using relativity, a stationary observer would see the piece of paper traveling at 890km/h. I pointed this out to my wife. I thought this was hilarious… –Her comment “You’re an idiot!”.

13. Michelson’s Experiment: A very important experiment was performed in the 1880's by Michelson and Morley. They designed a device called an interferometer which was supposed to find small differences in the speed of light.

15. Earth’s Speed: Situation A: –Earth is travelling towards the light sources with a velocity of 3.0 x 10 4 m/s Situation B: –Earth is travelling away the light sources with a velocity of 3.0 x 10 4 m/s

16. If relativity applied to all then: Situation A: –Light Speed + 3.0 x 10 4 m/s = speed of light observed Situation B: –Light Speed - 3.0 x 10 4 m/s = speed of light observed

17. The problem: There was NO difference between the observations of light’s speed. With no variation in light speed this would suggest that the Earth, the star, and the galaxy was not moving. This was known to be incorrect.

18. Postulate 1 : Absolute motion is not detectable. Postulate 2 : The speed of light is constant. Einstein suggested two postulates that changed physics. ***Remember Einstein’s life evolved around the movement of light and understanding how light worked!!! Nothing could go faster, and light always traveled at the same speed.

19. The first postulate is often stated in another form. That is; the laws of physics are the same for all observers that move at a constant velocity. The second postulate says that; no matter what the relative velocity is between the source of light and the observer of that light, the speed of light (c) will always be measured to be 3.00x10 8 m/s.

20. What does this mean? Time is also relative to speed. –As soon as there is motion in a system time is no longer a constant. Objects size must change at velocities to account for a constant light speed. –This is an effect called length contraction.

21. Consider the following: Let’s us a simple clock to explain time dilatation. Our clock will be a piston travelling upwards and downwards. The piston its self is traveling at light speed (We’ll discuss why soon) The piston hits it’s highest peak at time zero. A second later the piston is at it’s lowest position and so on….

22. Stationary Observer As the piston travels upwards and downwards the time is constant. No change provided the clock and the observer are travelling at the same rate of speed.

23. Time Dilation: Now let’s consider a situation where you are on a spaceship with that clock sitting in your ship. No matter how fast you travel, relative to you the clock will still be constant with your time since it is travelling at the same rate of speed as you.

24. Here’s where things get interesting:

25. Time measurement for you in the spaceship is the time it takes for the piston to complete one cycle.

26. Time measurement for observer is the triangular distance travelled by the piston.

28. The faster you travel: The greater the gap in velocity between you inside the spaceship and the observer.

29. The faster you travel: The greater the relative time differential.

30. It shows that the time an observer measures for an event on the spaceship, depends on the speed of the spaceship relative to the observer. The time t is larger than the time t o. This phenomenon is called time dilation. It is important to note that the times measured in both instances are made using identical clocks!

31. 3) The phenomenon of time dilation depends on the velocity of the spaceship relative to the observer. Find the time t (to 3 decimals) for an event on the spaceship as measured by an observer, if the time to for the event is 1.00 seconds. V (spaceship) t (observer) 0.010 c _____ 0.100 c_____ 0.500 c _____ 0.900 c _____ 0.990 c _____

32. How long would Mr. Jean’s best class ever take? Situation: Teaching a 10 minute physics class which is stationary. My relative speed to them would be 0.9999999999c

33. Returning Projects: We will continue into Chapter 17 next day. Topics to follow: –Length Contraction –Mass and Energy Relationship