lecture36 - last class-

lecture36 - last class- - our last class What you...

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Unformatted text preview: our last class What you will be able to do a/er today … Explain … Calculate … •  how to recognize an interference pa8ern arising from two ­slits that have a finite width •  The Rayleigh criterion needed to resolve two objects •  the diffracDon MINIMA •  the interference MAXIMA •  how many bright fringes are INSIDE the central bright band of a diffracDon pa8ern •  the parameters necessary for minimum resoluDon parameters Apply … •  the idea of wave interference in a single slit •  superposiDon of interference pa8erns •  concepts about how our eyes can ‘see’ detail WOW: Welcome OrientaDon for Women in Physics & Astronomy Interested in Physics or Engineering Physics? Want to know more about the programs that Physics & Astronomy has to offer? Not sure what career paths a Physics or Engineering Physics degree might take you on? Think physics is only for the guys?? No way! •  •  Join us on January 5, 2012 for a fun day and discover what Physics & Astronomy has to offer! Event includes: –  –  –  –  –  Build your own robot acDvity (limited space) DescripDon of various programs available Lunch! Panel discussion Lab tours Visit the website for more informaDon and registraDon: www.phas.ubc.ca/wow Stay tuned for informa=on updates on the website Chapt 22 Material •  Skipped – quanDtaDve intensity of Double Slit – page 676 ­677 (we only talked qualitaDve) •  Skipped Huygen’s Principle pg 681 •  Skipped Michelson Interferometer pg 688 ­690 •  Skipped Holography Masteringphysics •  Assignment 11 is not for marks, it relates to the last 2 week’s material – you should do the assignment. •  Look at the extra pracDce problems – some have “tutorials” (2.5 hours long) Leave your laptops at home Labs/Tutorials/Clickers •  These marks are being processed. •  Missing tutorial marks – email TA –  No response from TA – give me your assignment and I will update your mark •  Lab Exams  ­ marks are being entered –  All lab exams are being reviewed to ensure consistency in the marking •  Once all marks have been submi8ed by TAs then final lab mark will be available. •  trying to sync iclicker grades (random) demo: Rubens Tube visualizing a sound wave standing wave vibraDng in air Pressure fluctuaDons inside a hollow tube: pressure NODE – displacement ANTINODE pressure ANTI ­NODE – displacement NODE Two slit interference ONLY ONE WAVE gets through the slit at a Dme Diffraction Pattern MANY WAVEs going through the slit at the SAME Dme  these waves already start to interfere with each other p = 3 Double Slit Diffraction – Slits with finite width •  interference from the fact that there is TWO SLITS •  count BRIGHT fringes, mm = 2 •  diffracDon pa8ern from the fact that a SLIT has a WIDTH •  count DARK fringes, p m = 6 m = 5 m = 4 m = 3 m = 2 m = 1 m = 0 m=1 m = -1 •  the superposiDon of these pa8erns appear •  diffracDon minima envelope dominates interference pa8ern m = -2 m = 1 m = 2 m = 3 m = 4 m = 5 m = 6 p = 2 p = 1 m = 2 m = 1 m = 0 m = 1 m = 2 p = 1 p = 2 p = 3 The first diffraction minimum occurs at: a sin(θ ) = λ θ = sin −1 ȹ λ ȹ ȹ ȹ ȹ a Ⱥ CAN use small angle approximation sin(θ) = tan(θ) = θ y = λaL Position of first diffraction minimum Width of central maximum Angular Linear −1 2θ = 2sin (λ / a) 2 y = 2 λaL CombinaDon of separaDon of slits (d) and width of slits (a) gives you intensity pa8erns like In order to get a pa8ern like: d increases/decreases? a increases/decreases? Violet light of wavelength 400 nm passes through a single slit of width a and forms a diffraction pattern on the screen. If this light is replaced by orange light of wavelength 600 nm, the original diffraction pattern is reproduced if the slit width is changed to (A) (B) (C) (D) (E) a /2 a / 1.5 no change is necessary 1.5 a 2a Violet light of wavelength 400 nm passes through a single slit of width a and forms a diffraction pattern on the screen. If this light is replaced by orange light of wavelength 600 nm, the original diffraction pattern is reproduced if the slit width is changed to (A) (B) (C) (D) (E) a /2 a / 1.5 no change is necessary 1.5 a 2a Single Slit Diffraction -2.0 0 a 2.0 cm D Circular Apertures 16 Resolving Power of a Circular Aperture •  like your TWO EYES working together to disDnguish the features of one object •  like a camera lens trying to resolve the features of TWO objects Resolving Power of a Circular Aperture The images of two different objects are regarded as *just* resolved when the central diffraction maximum of one image coincides with the first diffraction minimum of the other. (Rayleigh criterion) θ min = 1.22 λ D If the distance is smaller, the two objects are not distinguishable ResoluDon of objects is quanDfied by Rayleigh Criterion λ D is the diameter of the lens/aperture θ min = 1.22 D θ=s/L is the angular separaDon, small angle sinθ=θ(rad) minimizing θ IMPROVES the resoluDon QuesDon For a given lens diameter, which color of light gives the best resolution in a microscope? (A) (B)  (C)  (D)  (E)  Red Yellow green blue white QuesDon For a given lens diameter, which color of light gives the best resolution in a microscope? (A) (B)  (C)  (D)  (E)  Red Yellow green blue white QuesDon Can your eyes resolve things better at night or during the day? (A) (B) (C) You can resolve things better at night You can resolve things better during the day You can resolve things the same during the day and night QuesDon Can your eyes resolve things better at night or during the day? (A) (B) (C) You can resolve things better at night You can resolve things better during the day You can resolve things the same during the day and night Your pupils become larger at night when there is less light, so increase D. Worksheet / QuesDon The Hubble space telescope orbits at 550 km above the surface of the earth. The primary mirror is D=2.5 m in diameter. Suppose the telescope is pointed towards the Earth and it is looking at visible light with λ=500 nm What is the smallest thing that can be resolved? A) Football stadium s sin ! ! ! = B) Car L C) Basketball ! ! min = 1.22 D) Grasshopper D E) Flea Ans. 13 cm. So something just slightly bigger would be visible. ApplicaDon of diffracDon Feel free to stop by and/or email : heiner@phas.ubc.ca Hennings rm. 405 $10 $5 $5 $5 $10 ...
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