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- Indiana
- Purdue University
- Physics
- Physics 221
- Bortoletto
- db_lec19_post.pdf

Roman W.

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LHC HAS RESTARTED DATA TAKING MARCH 30 2010 D. Bortoletto PHYS221 1 LIKE GALILEO POINTING HIS TELESCOPE TO THE SKY FOR THE FIRST TIME IN 1608 FOLLOW ON: TWITTER/FACEBOOK/WWW LHC TV LECTURE 19: Interference, Diffraction, Resolution http://antwrp.gsfc.nasa.gov/apod/image/0507/47tuc_chandra_f.jpg 2D. Bortoletto PHYS221 Interference • Three ways in which the phase difference between two waves can change: 1. By traveling though media of different indexes of refraction 3 2. By traveling along paths of different lengths 3. By reflection from a boundary D. Bortoletto PHYS221 Interference: Double Slit • The phase difference between two waves can change if the waves travel paths of different lengths. Interference maxima for d sinθm = mλ, m = 0,1,2,... 4 Interference minima for d sinθm = m + 12 λ, m = 0,1,2,... D. Bortoletto PHYS221 Interference: Double Slit (DEMO) He, Ne laser 5 two slits Laser (Light Amplification by Stimulated Emission of Radiation) D. Bortoletto PHYS221 Diffraction • If light of wavelength λ falls on an object of dimension d and d≈λ, geometrical optics is no longer a good approximation. • Let us consider the case of light impinging on a small disk. We observe: 6 1) bright spot in the center. 2) diffraction rings outside and inside the geometrical shadow area • The bright spot at the center was predicted by Fresnel in 1818 and observed by Arago. D. Bortoletto PHYS221 Diffraction from a Disk Geometrical Optics (black lines) 7 In wave optics (red lines) the two waves that touch the top and bottom of the disk travel the same distance to the center and therefore interfere constructively D. Bortoletto PHYS221 Fresnel Diffraction plane wave intensity 8 center bright spot: consistent only with wave theory. cylindrical obstacle Counter-intuitive result! D. Bortoletto PHYS221 Diffraction (DEMO) diffraction plane wave obstacle 9 pattern D. Bortoletto PHYS221 Diffraction from a Single Slit • Consider a monochromatic wave incident on a place with a narrow slit. • Geometrical optics predicts that the transmitted beam has the same cross section of the slits • Experiments show that wave optics is 10 correct and that: 1) there is a central bright band that is wider than the width of the slit 2) Alternating dark and bright fringes border the central bright band D. Bortoletto PHYS221 Diffraction from a Single Slit 11D. Bortoletto PHYS221 Diffraction from a Single Slit Represent the slit as a number of point sources of equal amplitude. Divide the slit into two and pair a point from the upper half with its partner in the lower half. 12 occurs. rays paired the between ceinterferen edestructiv ,21sin21 When λθ =aθsin 2 a D. Bortoletto PHYS221 Diffraction from a Single Slit ,...3,2,1,sin :ndiffractioslit -singlefor minima of Locations m == mma λθ m mtan m y Lθ θ≈ = 13D. Bortoletto PHYS221 1 1sin a λθ θ≈ = Smaller a ⇒ Bigger θ1 and y1 Diffraction from a Single Slit smaller aperture, diffraction broadening 14 larger aperture, less flaring of light D. Bortoletto PHYS221 Diffraction from a Single Slit (DEMO) laser ⇐Intensity 15 Secondary maxima are weak. plane wave with wavelength λ slit width a D. Bortoletto PHYS221 CQ1 We produce a diffraction pattern on a viewing screen by using a long narrow slit illuminated by blue light. Does the pattern expand away from the center or contract toward it if we switch to yellow light? 16 (A) Expand away from it (B) Contract toward it D. Bortoletto PHYS221 Diffraction from a Circular Aperture (DEMO) The diffraction pattern of a circular aperture of diameter D is similar to a single slit of width a. • The central bright spot is called Airy disk. About 85% of the power is in this area. • The dark fringes are found at: 17 1 2 3 sin 1.22 sin 2.23 sin 3.24 D D D λθ λθ λθ = = = D. Bortoletto PHYS221 Diffraction from a Circular Aperture The bright fringes are at: 1sin 1.63 sin 2.68 D λθ λθ = = 18 The Airy disk limits the resolvability of nearby objects 2 3sin 3.70 D D λθ = Image of two nearby binary stars D. Bortoletto PHYS221 Rayleigh Criteria • The minimum angular separation θmin of two marginally resolvable points is such that the maximum of the diffraction pattern from one falls on the first minimum of the diffraction pattern of the other, • The first minima is at sin 1.22 λθ = 19 D min 1sin 1.22 1.22 D D θ θ λ λ− = = ≈ Therefore D. Bortoletto PHYS221 Rayleigh Criteria If θ> θmin objects can be resolved If θ< θmin objects can not be resolved To increase our ability to distinguish objects we must minimize the diffraction pattern. Because min 1.22 D λθ ≈ 20 we can : increase D or decrease λ 1) Use ultraviolet light 2) e- beam used in Scanning Electron Microscopes (SEM) have λ≈λ(light)/105 3) place object under a microscope in a drop of oil λn=λ/n D. Bortoletto PHYS221 Rayleigh Criteria θ 21D. Bortoletto PHYS221 θ Diffraction Gratings • What happen if we go from 2 slits to N slits ? • The fringes become narrower and faint secondary maxima appear between the fringes ( half-width of central line). • If N is large (N/ℓ≈104/cm) the fringes are very sharp and the secondary maxima can be neglected and you have a grating. ∆θhw = λNd 22 d δ θθ θδ sin 10250001 5000)( 4 ddifferencepathlength cmcmdNcmd cm lines cm linesNrulings spacinggratingd == ×= == =⇒ = − D. Bortoletto PHYS221 • Sharp bright fringes occur if where m is the order of the maxima. • Grating are used to measure λ Diffraction Gratings (DEMO) 2,1,0sin === mmd λθδ λ 23 by detecting maxima of the diffraction pattern with m=1,2,… • Resolving power dmθ =sin R mNλλ= =∆ D. Bortoletto PHYS221 Diffraction Gratings (DEMO) 24D. Bortoletto PHYS221 CQ2 The Rayleigh criterion determines the ultimate resolution of a telescope. If the diameter of the telescope aperture is increased does θmin (A) get smaller 25 (B) get larger (C) stays the same D. Bortoletto PHYS221 bortolet

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