PHYS 202. Lecture 18 Professor Stephen Thornton April 4, 2006

Transcription

1 PHYS 202 Lecture 18 Professor Stephen Thornton April 4, 2006

2 Reading Quiz: Can light, say visible light, bend around corners? 1) Yes. 2) Sometimes, but it depends on the wavelength. 3) Sometimes, but it depends on the frequency. 4) No, not since 1802.

3 Answer: 1 Yes, it is called diffraction.

4 Last Time Superposition of waves Interference of waves Young s two-slit experiment Phase change due to reflection Interference effects Newton s rings, thin films, etc. Single-slit diffraction

5 Today Single slit diffraction Poisson spot Multiple slit diffraction Resolution Diffraction gratings Applications

6 Diffraction of Water Waves Does the same thing occur for light? Does light bend around corners?

7 Show razor edge diffraction demo

8 Single-Slit Diffraction We did demo last time.

9 Locating the First Dark Fringe in Single-Slit Diffraction W λ sinθ = 2 2 W sinθ = λ

10 W λ = Single slit diffraction = slit width θ = angle wavelength Wsinθ = mλ m=± 1, ± 2,... *** This is when destructive interference occurs. Dark spots. The bright spots will be about halfway between. 2λ Angular width of central fringe θ = *** W

11 Single slit central beam

12 Single slit first dark fringe

13 Single slit intensity Angular width = 2 λ /W

14 Conceptual Quiz: In single slit diffraction, what happens if we make the slit narrower? 1) The central peak is sharper and easier to see. 2) The first maximum is seen at a smaller angle and is brighter. 3) The first maximum is seen at a smaller angle and is not as bright. 4) The first maximum is seen at a larger angle.

15 Answer: 4 The central peak becomes wider and more spread out as the slit width is more narrow. The first maximum has sinθ ~ 1/W, so the angle increases as W becomes smaller.

16 Shadow of a penny

17 There is a fascinating story about the origin of this experiment, referenced from Eugene Hecht, Optics (Second Edition) and at the web site Fresnel Diffraction, written by Dean Dauger: In 1818, Augustin Fresnel submitted a paper on the theory of diffraction for a competition sponsored by the French Academy. His theory represented light as a wave, as opposed to a bombardment of hard little particles, which was the subject of a debate that lasted since Newton's day. Siméon Poisson, a member of the judging committee for the competition, was very critical of the wave theory of light. Using Fresnel's theory, Poisson deduced the seemingly absurd prediction that a bright spot should appear behind a circular obstruction, a prediction he felt was the last nail in the coffin for Fresnel's theory. However, Dominique Arago, another member of the judging committee, almost immediately verified the spot experimentally. Fresnel won the competition, and, although it may be more appropriate to call it "the Spot of Arago," the spot goes down in history with the name "Poisson's bright spot" like a curse.

18 Poisson s or Arago s spot Do demo

19 Single, small circular opening

20 Resolution 2 objects Diameter D A useful criteria is to have the dark fringe of one object be at the center of the peak for the second object for minimum resolution. Circula opening, position of first dark fringe λ sinθ = 1.22, D λ θ = 1.22 min *** D The larger D, the better resolved. Called Rayleigh s criterion.

21 Resolution 2 objects Well resolved Barely resolved Not resolved θ min Object is too far away, and angular separation is too small for our eyes.

22 Eagle eyes Work example for eagle and human.

23 Resolution 2 objects (for example, car headlights, 2 m apart) Well resolved Barely resolved Not resolved Need at least twice the resolution. Maybe 3-4 km. Our calculation indicates 7 km - doubtful Object is too far away, and angular separation is too small for our eyes.

24 Television screen

25 Pointillism Painting consists of small dots of color on canvas. Henri Edmond Cross Georges Georges Seurat Seurat

26 Sunday in the Park by Georges Seurat 81 x 120 inches; 2 years to complete; ~ 4 megadots

27 Conceptual Quiz: You are designing a spy satellite to look for humans during the day. For the best resolution by the human eye, which of the following EM radiations should you use? 1) ultraviolet light 2) blue light 3) yellow light 4) red light 5) infrared light See hint on next slide.

28 Conceptual Quiz: You are designing a spy satellite to look for humans during the day. For the best resolution by the human eye, which of the following EM radiation should you use? 1) ultraviolet light 2) blue light 3) yellow light 4) red light 5) infrared light θ = 1.22 min λ D

29 Answer: 2 Remember that the angular resolution depends directly on λ, so you should use the smallest wavelength. That would be ultraviolet, but humans cannot see ultraviolet light, so you should choose blue light. Many spy satellites use infrared light, so they can see at night.

30 Hubble Space Telescope and Spy Telescopes For a mirror of 2.4-m diameter, like in HST and spy telescopes, the θ min for visible light is 2 x 10-7 rad. So if the telescope is 400 km above the Earth, it can resolve objects 8 cm apart. The French Spot telescope will sell anyone images with 2.5 m resolution. Canberra, Australia 2.5 m resolution

31 Quickbird image. 0.6 m resolution. Wellington stadium in NZ

32 Look at Google Earth University of Virginia White House U.S. Capitol Jefferson Memorial

33 Diffraction grating multiple slits

34 Path-Length Difference in a Diffraction Grating dsin θ = mλ *** m = 0, ± 1, ± 2,... For constructive inteference

35 Diffraction Pattern for Five Slits

36 Do multiple slit demo

37 Comparison 2 and 5 slits Advantages of Multiple slits N: Intensity increases as N 2 The width of a peak ~ 1/N

38 Intensity comparison of 2, 4, 10 slits

39 Reflection from a CD Actual photo Try demo on Elmo

40 Reading CDs Destructive interference occurs when λ/2 of the laser beam equals 2t. There is then much less reflection at the pit edge, which denotes the signal. t

41 A Grating Spectroscope

42 X-ray diffraction Slit openings are tenths of nm. Need wavelength of same order. Must use x-rays.

43 DNA Francis Crick (NP, 1962) James Watson Rosalind Franklin (died at age 37 in 1958)

44 Work problems 28-64, 28-65