Prozorov_32 - PHYSICS 222 Introduction to Classical Physics...

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Unformatted text preview: PHYSICS 222 Introduction to Classical Physics II Prof. Ruslan Prozorov Iowa State University Fall 2011 LECTURES 32 Diffraction. Diffraction grating. Limits of optical resolution. Fresnel and Fraunhofer diffraction According to geometric optics, a light source shining on an object in front of a screen will cast a sharp shadow. Surprisingly, this does not occur. PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 2 Light bends around the corner Huygens’ model: each point in the wavefront emits a wavelet. obstacle • • Block the lower sources of induced fields with an obstacle Induced fields from upper sources/wavelets are still spherical – reach beyond blockage – waves effectively “bend” around corners PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 3 Diffraction and Huygen’s Principle • Diffraction patterns can be analyzed using Huygen’s Principle. Recall, every source of a wave front can be considered to be the source of secondary waves. Superposition of these waves results in diffraction. • If the source and the screen are close to the edge causing the diffraction, the effect is called “near-field” or Fresnel diffraction. If these objects are far apart, so as to allow parallel-ray modeling, the diffraction is called “far-field diffraction” or Fraunhofer diffraction. PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 4 AM/FM radio Examples: AM signal with f = 1000 kHz λ = 300 m FM signal with f = 100 MHz λ=3m In mountainous areas, AM radio station reception is much better because AM waves are diffracted “around” the mountain tops and into the valleys FM waves propagate “in a straight line” and cannot reach the valleys (unless an antenna on top of the mountain is used) PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 5 Your roommate’s music Like interference, diffraction applies to ALL waves (not just light) Human ear perceives f ~ 20 Hz – 20 kHz λ ~ 2 cm – 2 m A door left ajar (opening ~ 1-5 cm) protects you from most of your roomie’s music, but not from the bass track. (same applied to cars with ajar windows) Also: That’s why all home theater speakers must be “in line of sight”, but subwoofers can be behind the sofa. PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 6 diffraction from a single slit PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 7 intensity in a single-slit pattern PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 8 dark fringes in single-slit diffraction PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 9 single-slit diffraction Slit of width a • consider it made of a large number of point sources • interference by N sources P N sources -> N phasors θ a R >> a Angle between first and last phasors: PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University ka sin 2 a sin 9 November 2011 10 Length of the arc is NE0 = Emax (amplitude when β = 0) r β/2 r β/2 EP E max r (β in radians) From the triangle: β E0 EP 2r sin E max 2 sin 2 2 r E P E max sin 2 2 PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University EP sin 2 2r E max 2 sin 2 IP I max 2 9 November 2011 11 Minima: 2m m 1, 2... a sin m m 1, 2... Maxima: ( I I max ) b » 2m + 1 p sin 2 2 2 (and b = 0) θ This is the “normal” part PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University This is light “bending around the corner”! 9 November 2011 12 intensity maxima in a single-slit pattern PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 13 Fresnel or Fraunhofer limit? 2 a F x F 1 F 1 Fresnel diffraction (near-field diffraction) Fraunhofer diffraction (far – field diffraction) - diffraction pattern is viewed at a long distance from the diffracting object, and also when it is viewed at the focal plane of an imaging lens. PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 14 Fraunhofer limit PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 15 example: Fraunhofer diffraction =600 nm y1 x 16 mm a 600 109 a=6.0 0.255 mm 3 16 10 PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 16 diffraction and wavelength Diffraction effects (= light bending around the corner) are most important when a ~λ Diffraction pattern of a square slit (with both sides a ~λ) PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 17 rectangular slit PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 18 circular opening (Airy pattern) PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 19 Interference from multiple slits • The approximation of sin θ = θ is very good considering the size of the slit and the wavelength of the light. PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 20 Multiple slit interference • The analysis of intensity to find the maximum is done in similar fashion as it was for a single slit. PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 21 PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 22 several slits interference PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 23 PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 24 realistic double-slit We need to take diffraction into account! Superposition of interference and diffraction effects: Interference: Diffraction: The total output: IP Imax cos 2 2 sin 2 IP I max 2 2 d sin 2 2 sin 2 2 IP I max cos 2 2 PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University a sin 2 9 November 2011 25 d Two slit interference MAXIMUM when sin m d Each slit diffraction MINIMUM when sin m a a Interference pattern modulated by diffraction pattern (with d >>a ) PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 26 0 –1 1 –2 –3 (–5) –4 PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 2 3 4 (5) 9 November 2011 27 the diffraction grating Two slits change the intensity profile of interference; many slits arranged in parallel fashion produce grating. PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 28 PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 29 PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 30 PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 31 PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 32 The grating spectrograph A grating can be used like a prism, to disperse the wavelengths of a light source. If the source is built of discrete wavelengths, we have spectroscopy. Chemical systems and astronomical entities have discrete absorption or emission spectra that contain clues to their identity and reactivity. PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 33 The grating spectrograph example PHYS222 - Lecture 32 - Prof. Ruslan Prozorov - Iowa State University 9 November 2011 34 ...
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This note was uploaded on 11/14/2011 for the course PHYS 5863005 taught by Professor Meyer during the Fall '09 term at Iowa State.

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