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Chapter 27 Physical Optics Interference and the Wave Nature of Light 0. Waves • Disturbance propogating through space 1. Linear Superposition Resultant disturbance from 2 waves is sum of individual disturbances a) Constructive Interference (b) Destructive interference 2. Young’s Double Slit, 1801 - the first definitive evidence of the wave-nature of light a) The phenomenon QuickTime™ and a TIFF (U ncompressed) decompressor are needed to see this picture. See applet at www.falstad.com b) The concept c) The equation When l m constructive interference (m 0,1,2...) When l (m 1 2) destructive interference (m 0,1,2...) From the geometry, l dsin , so m dsin bright fringe (m 12) dsin dark fringe m dsin bright fringe (m 12) dsin dark fringe White light interference 3. Thin film interference a) The phenomenon & concept • 1, 2 travel different paths • interference possible • depends on wavelength (color) • depends on thickness (pattern) • depends on angle (pattern) b) The equations Constructive Interference: (Eff. path length) m Destructive Interference: (Eff. path length) (m 12) Contributions to Eff. path length: (i) Geometrical path length = 2t (ii) Optical path length OPL = eq’t distance traveled in vacuum For distance 2t, 2t c2t OPL c 2nt v c /n Or use wavelength in medium: film vacuum n (iii) Phase change for increasing n 2 (Eff. Path Length) = OPL EPL = 2n filmt 2 2 (one phase change) (one phase change) Constructive Interference: EPL m 1 EPL (m Destructive Interference: 2) 4. Michelson Interferometer • Used to measure wavelength If DA DF , constructive interference If DA DF 4 , destructive interference If DA DF m 2 , constructive interference • Adjust DA by measured amount (y) and count (N) bright-dark cycles: y 2N 5. Diffraction a) Huygen’s principle, 1678 Every point on a wave front acts as a source; the advancing front is the sum of waves from each source. Effectively, the tangent of the point-source waves forms the advancing front b) Diffraction phenomena Waves bend around obstacles. Depends on ratio: W W Diffraction pattern observed QuickTime™ and a TIFF (U ncompressed) decompressor are needed to see this picture. c) Equation for minima Bright fringe at = 0 First dark fringe sin W 1, 3 cancel 2, 4 cancel Each ray in upper half cancels a ray in lower half Second dark fringe 2 sin W Equation for dark fringes: Each ray in 1st quarter cancels a ray in the second quarter; each ray in the 3rd cancels one in the fourth. m W sin Diffraction pattern: Central fringe is brightest because all rays interfere constructively. QuickTi me™ and a TIFF (Uncompressed) decompressor are needed to see this picture. Example: Problem 27-27 Width of central fringe is 450 times slit width. Find W if the distance to the screen is 18000W. 6. Resolving Power a) The concept Diffraction at the apertures in optical instruments (pupil), limit resolving power. b) Diffraction at circular aperture sin 1.22 D QuickTime™ and a TIFF (U ncompressed) decompressor are needed to see this picture. D c) Rayleigh Criterion Objects resolved when first dark fringe of one coincides with the central bright fringe of the other min 1.22 D Example: Human and Eagle eyes (a) Find minimum s for human (D = 2.5 mm) (b) Find minimum s for eagle (D = 6 mm) d) “Absurd” diffraction around a circular obstacle In 1818, the young Fresnel entered his wave theory in a competition sponsored by the French Academy. Poisson, one of the judges, predicted a bright spot at the centre of the shadow of a disc, based on Fresnel’s theory. “Such an absurdity must surely disprove the entire theory!” Arago, another judge, went to the laboratory, and saw the absurd. … paraphrased from Hecht, Physics Diffraction around a pushpin image QuickTime™ and a TIFF (U ncompressed) decompressor are needed to see thi s picture. pin Laser 7. Diffraction grating a) 2-slit interference m dsin for maxima (m 1 2) d sin for minima (b) 3-slit interference For (m 12) dsin adjacent slits cancel y1 sin( x) m dsin for principal maxima QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. y2 sin( x ) QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. y3 sin( x 2 ) QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. y y1 y2 y3 QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. Resultant is not zero. Complete cancellation occurs when waves are offset by 3. --> 2 minima between principal maxima: QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. (c) N-slit interference (diffraction) 4 slits QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. 5 slits QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. 50 slits QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. QuickTi me™ and a TIFF ( Uncompressed) decompressor are needed to see thi s pi ctur e. (d) Separating colors m dsin for principal maxima (e) The grating spectroscope (f) Diffraction patterns to probe structure Examples: - difference in diffraction angles from CDs and DVDs - diffraction pattern to determine thickness of hair - diffraction pattern from complex gratings (textiles etc) - principle of holography 8. Interference and optical media Pit thickness t = 4 giving destructive interference in beams reflected from edges. Variation in intensity used to read binary data. Two tracking beams produced by a diffraction grating are used to follow the flat region between tracks. 9. X-ray diffraction Regular arrays of atoms produce diffraction patterns, for short wavelength radiation (Xrays). This diffraction pattern produced by Rosalind Franklin in 1953 helped determine the structure of DNA. The method is used routinely for structural determination.