浙江大學大學物理甲下 chapter 43

1、Chapter 43 Gratings and Spectra8/10/2022143-1 Multiple Slits8/10/202228/10/202238/10/20224 1. The spacing of the fringes is determined by the slit separation d, independently of the number of slits. The fringes are sharper (narrower), when the number of slits increases. 2. The faint secondary maxima

2、 appear between adjacent bright fringes. As the number of slits increases, the number of secondary maxima increases but their brightness decreases.Grating: the number of slits N may be as large as 104 per cm.8/10/20225 The location of principal maxima is determined by:Principal maximad is slip separ

3、ation, also is called grating constant (grating spacing).8/10/20226 Secondary maxima There are some minima between two principal maxima.Superposition of some phasors8/10/202273 slipsThere 2 minima between two principal maxima. 1231238/10/202284 slipsThere 3 minima between two principal maxima. 8/10/

4、20229 If the grating has N slips, there are N-1 minima between two principle maxima. There is a secondary maximum between two minima. If the grating has N slips, there are N-2 secondary maxima between two principle maxima. Thus the more the slips are, the more the secondary maxima are, the more thin

5、 the principle maximum is. 8/10/202210N=2N=3N=4N=5N=10Between 2 principal maxima:N-1 minima, N-2 maxima8/10/202211 Width of the principle maxima For the first minimum of zero intensity, the phase difference between waves from adjacent slits isFor central principal maximum, its width can be represent

6、ed by . (Figure 43-5)72N=5N=28/10/202212The corresponding path difference between adjacent slits isThe maxima becomes sharper.8/10/202213For the width of mth principal maximum (figure 43-5)Nd is the total width of the grating. As Nd is increasing, the is decreasing, the maxima become sharper.8/10/20

7、2214 Intensity distribution 8/10/202215I/I0I/I0I/I0I/I0single-slit diffraction double-slit interferencedouble-slit diffraction grating diffraction8/10/202216 Missing order m1th fringe is not seen, this is missing principle maxima.I/I05th principle maximum is missing because d/a=5. And 10th,15th,also

8、.8/10/20221743-2 Diffraction gratingsTransmission gratingReflection gratingA compact disk is a diffraction grating.8/10/202218* screen VERY far awayqDiffraction Grating8/10/202219Spectrum of light central1st (m=1)2nd (m=2)3rd (m=3)Prism SpectroscopeContinuous spectrum (band spectrum)Line spectrum8/1

9、0/202220Grating spectroscope and spectrographsSpectral lines (Fig 43-9)8/10/202221 The spectrometer is a useful tool in atomic spectroscope, in which the light from an atom is analyzed to find the wavelength components. These wavelength components can be used to identify the atom. The atomic spectra

10、 is a key, with it we can investigate the mystery of the atoms. 8/10/202222From top to bottom, emission spectra of barium, calcium, hydrogen, and sodium and a solar absorption spectrum.8/10/202223Example: A grating (N=5000) is illuminated by two monochromic lights with wave lengths of 600 and 400 nm

11、 respectively. The mth principal maximum of the former light is meet the (m+1)th principal maximum of the later at 3cm from the central fringe on the screen. The focus length of the lens is 50cm. Find the grating constant d, and the typical width of the principle fringes. Solution:8/10/2022248/10/20

12、2225Quick quiz Ultraviolet light of wavelength 350nm is incident on a diffraction grating with slit spacing d and forms an diffraction pattern on a screen a distance L away. The angular positions bright of the interference maxima are large. The locations of the bright fringes are marked on the scree

13、n. Now red light of wavelength 700nm is used with a diffraction grating to form another diffraction pattern on the screen. The bright fringes of this pattern will be located at the marks on the screen if (1) the screen is moved to a distance 2L from the grating. (2) the screen is moved to a distance

14、 L/2 from the grating. (3) the grating is replaced with one of slit spacing 2d. (4) the grating is replaced with one of slit spacing d/2. (5) nothing is changed. 8/10/20222643-3 Dispersion and resolving power The ability of a grating is determined by two intrinsic properties of the grating: (1) d ;

15、(2) N , the number of slits.Sample problem 43-2: 8/10/202227DispersionResolving power If the maximum of one lines falls on the first minimum of its neighbor, we should be able to resolve the lines.not resolved resolvedjust resolved8/10/202228Resolving power R8/10/202229Sample problem 44-3:N=9600, W=

16、3.00cm, line spectrum of mercury vapor.8/10/20223043-4 X-ray DiffractionX-ray: =0.11nm.Laue experimentLaue spots8/10/202231 in NaCl d 1st maximum will be at 10Crystal solid such as sodiumConstructive interference:8/10/202232 Braggs lawDetermination of crystalline structures8/10/202233 There are many

17、 other such planes with different interplanar spacing. If an incident monochromatic x-ray falls at an multi-crystals, there are d and which satisfied Braggs law certainly in crystal. (Debye manner) If an incident x-rays they are continuous in wavelength falls at a single-crystal, there are and which

18、 are satisfied Braggs law certainly in the crystal. (Laue manner)8/10/202234Sample problem 43-5: =0.110nm, a0=0.563nm,If a diffraction beam is to exist,8/10/20223543-5 Holography 8/10/202236film objectlightreference beamvirtual imagereal imagehologramTransmission light8/10/202237Normally pictures (photographs) record light intensities from the object.Holography: recording both the intensity and phase of the waves (light) from object. Three dimensio