Physics A2 - Lecture 4: Applications of interference and diffraction - Huynh Quang Linh

Nội dung text: Physics A2 - Lecture 4: Applications of interference and diffraction - Huynh Quang Linh

1. Lecture 4:Applications of interference and diffraction Rosalind Franklin made the first x-ray diffraction imaging of DNA; her pictures were instrumental in the discovery of the double-helix structure.
2. X-ray Crystallography The Braggs made so many discoveries that Lawrence described the first few years as ‘like looking for gold and finding nuggets lying around everywhere’: • showed that the sodium and chloride ions were not bonded into molecules, but arranged in a lattice • could distinguish different cubic lattices • discovered the crystal structure of diamond • Lawrence Bragg was the youngest Laureate ever (25) to receive a Nobel Prize (shared with his father in 1915) • now standardly used for all kinds of materials analysis, even biological samples! • The same multi-layer interference phenomenon is now used to make highly wavelength-specific mirrors for lasers (“distributed Bragg feedback” [DBF])
3. Transmission of light through slits and circular apertures 1 1I0 diff (x)I0.5 Observation Slit, screen: 0 00 10-l/a 00 l/a 10 q width a 12.56 x 12.56 Monochromatic light 1 source at a great 1I0 distance, or a laser. diff (x)I0.5 Pinhole, Observation 0 00 diameter D screen: 10 0 10 q 12.56-1.22l/D 0x 1.22l/D12.56 1I1 Object at any 0 distance: diff (x)I0.5 Image Plane: Lens, 0 00 diameter D 10 0 10 q 12.56-1.22l/D 0x 1.22l/D12.56 Laser with pinholes Circular-aperture diffraction pattern =“the Airy disk”. Central lobe contains 84% of power.
4. Exercise 1: Expansion of a Laser beam In 1985, a laser beam with a wavelength of l = 500 nm was fired from the earth and reflected off the space shuttle Discovery, in orbit at a distance of L = 350 km away from the laser. d D 1. If the (circular) aperture of the laser was D = 4.7 cm, what was the beam diameter d at the space shuttle? -9 Half-angle-width of l 500 10 -5 q =1.22 = 1.22 = 1.3 10 radians 84% of diffraction maximum: o -2 D 4.7 10 power is in central -53 d 2 qo L = 2(1.3 10 )(350 10 m) = 9.1 m lobe. 2. To make a smaller spot on the shuttle, what should we do to the beam diameter at the source? a. reduce it Counter-intuitive as this is, it is correct – you b. increase it reduce beam divergence by using a bigger c. cannot be made smaller beam. (Note: this will work until D ~ d)
5. Exercise 2: Focusing of a laser beam There are many times you would like to focus a laser beam to as small a spot as possible. However, diffraction limits this. Dlens Dlaser d f 1. The (circular) aperture of a laser (l = 780 nm) has Dlaser = 5 mm. What is the spot-size d of the beam after passing through a (perfect) lens with focal length f=5mm, diameter Dlens = 6 mm? (Hint: light passing through lens center is undeflected.) The angular spread of the beam is determined qlo=1.22 / D laser by the smaller of Dlaser and Dlens: Light at this angle will intercept the focal plane at d/2 ~ f qo: d 2 qo f = 2.44 l f / D laser = 2.44(0.78  m)(5mm) /(5mm) = 1.9  m 2. Which of the following will reduce the spot size? a. increase l Since the diffraction is already limited by D, b. decrease l increasing dlens doesn’t help. c. increase d There is a huge industry devoted to developing lens cheap blue diode lasers (l ~ 400 nm) for just d. decrease dlens this purpose, i.e., to increase DVD capacity.
6. Example: Angular resolution Car headlights in the distance: What is the maximum distance L you can be from an oncoming car at night, and still distinguish its two headlights, which are separated by a distance d = 1.5 m? Assume that your pupils have a diameter D = 2 mm at night, and that the wavelength of light is l = 550 nm.
7. exercise 3: Resolving Stars Halley’s Comet 1. Assuming diffraction-limited optics (best possible), what is the minimum angular separation of two stars that can be resolved by a D = 5 m reflecting telescope using light of l = 500 nm? a. 0.1 rad b. 1 rad c. 10 rad 2. If the two points are not quite resolved at screen 1, will they be resolved at screen 2? screen 1 screen 2
8. Optical Interferometers Interference arises when there are two (or more) ways for something to happen. Ex. Two slits for the light to get from the source to the screen. 2 I = 4I1 cos (/2), with  = 2p d/l, and path-length difference d. An interferometer is a device using mirrors and “beam splitters” (half light is transmitted, half is reflected) to give two separate paths from source to detector. Two common types: Mach-Zehnder: Michelson : beam- splitter mirror mirror beam- splitter
9. exercise 4 Consider the following Michelson interferometer. d Assume that for the setup shown, all the light (with l = 500 nm) comes out the bottom port. 1. How much does the top mirror need to be moved so that none of the light comes out the bottom port? (a) 125 nm (b) 250 nm (c) 500 nm 2. Where does the light go?
10. Questions 1) Could you construct a diffraction grating for sound? If so, what grating spacing is suitable for a wavelength of 0.5 m? 2) Discuss this statement:”A diffraction grating can just as well be called an interference grating”
11. Simulation lab of diffraction Present and discuss