Chapter 24 Wave OpticsSlide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14A prism also disperses lightSlide 16Slide 17Slide 18Chapter 24Chapter 24Wave OpticsWave Optics Diffraction Grating Diffraction Grating Interference by Thin FilmsInterference by Thin FilmsPolarizationPolarizationdExtra distance msin=m/d or dsin=mm 2 Constructive inferencem=1/2,3/2,5/2, . . . Destructive inferenceExample: In a double-slit experiment it is found that blue light of wavelength 460 nm gives a second-order maximum at a certain location on the screen. What wavelength of visible light would have a minimum at the same location? Answer: For constructive interferenced sin=m=2x460nm=920nmFor destructive interference of the other light, we have d sin=(m’+1/2)When the two angle are equal, then 920nm=(m’+1/2) =1.84x103 nm for m’=0 =613 nm for m’=1 =368 nm for m’=2The only wavelength here that is visible is 613 nmWhen a light wave travels from one medium to another, its frequency does not change, but its wavelength does:v2t/v1t=v2/v1=n1/n2 (v=c/n) n1/n2 = 2= sin(r)/sin(i)The shorter the larger refraction angleExample: Monochromatic yellow light illuminates two narrow slits 1 mm apart the screen is 1 m from the slits, and the distance from the central bright light to the next bright line is found to be 0.589 mm. Find the wave length of the light.Solution: d sin=mwhere m=1ord sin (1x10-3m)(5.89x10-4m)/1m= 5.89x10-7 m =589 nm 1 m1 mm 0.589 mmThere are two difficulties in using a double slit for measuring wavelengths. 1. The bright linesbright lines on the screen are actually extremely faintfaint and an intense light source is therefore required;2. The lines are relatively broad and it is hard to locate their center accurately.A diffraction grating that consists of a large number of parallel slits overcomes both of these difficulties. A diffraction grating uses interference to disperse light. It is often an important component in optical instrumentation for wavelength determinations.Diffraction GratingDiffraction Gratingdsin=mm 2 Constructive inferencem =1/2,3/2,5/2, . . . Destructive inferenceFor a diffraction grating, the intensity falls away from these maxima much more rapidly than that for a double slit. Because there are so many slits to act as sources, any angle other than those for maxima will be dark or nearly dark.Example: Visible light includes wavelengths from 4x10-7 m to 7x10-7m. Find the angular width of the first-order spectrum produced by a grating ruled with 800 lines/cm. Solution: The slit space d that corresponding to 800 line/cm is d=(10-2 m/cm)/(8x103 lines/cm)=1.25x10-6 mSince m=1, sinb=b/d = 4x10-7m/1.25x10-6m = 0.32, b=19osinr=r/d = 7x10-7m/1.25x10-6m = 0.56, r=34oThe total width of the spectrum is therefore 34o-19o=15o The angle can be measured to very high accuracy, so the wavelength of a line can be determined to high accuracy using =d sin/mQuestion: A characteristic property of the spectra produced by a diffraction grating is (a) the sharpness of the bright lines(b) diffuseness of the bright lines(c) absence of bright lines (d) absence of dark lines Answer: aQuestion: The greater the number of lines that are ruled on a grating of given width,(a) The shorter the wavelengths that can be diffracted(b) The longer the wavelengths that can be diffracted(c) The narrower the spectrum that is produced(d) The broader the spectrum that is producedAnswer: dSpectrometer and SpectroscopySpectrometer and Spectroscopyusing a grating or prismusing a grating or prismA prism also disperses lightA prism also disperses lightn1/n2 = 2/= sin(r)/sin(i)Question: White light strikes (a) a diffraction grating, and (b) a prism. A rainbow appears on a screen just below the direction of horizontal incident beam in each case. What is the color of the top of the rainbow in each case?Answer: (a) Violet for diffraction grating (m=dsin) (b) Red for prism (n1/n2 = 2)Light from all parts of the slit travels the same distance and arrives "in phase" so there is a bright central maximum. Single-slit DiffractionSingle-slit DiffractionA single slit diffraction pattern has a bright central maximum surrounded by much smaller maxima. A Single-slit Diffraction IntensityA Single-slit Diffraction
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