The Wave Nature of Light Physics 102 Lecture 7 4 April 2002 Pick up Grating & Foil & Pin 4 Apr 2002 Physics 102 Lecture 7 1
Light acts like a wave! Last week we saw that light travels from place to place along rays that trace paths as particles would. Geometric optics: However, light also produces interference patterns just like sound or water waves. Wave optics: Young (as in Young s Modulus) demonstrated interference of light in 1801 using a double slit apparatus. 4 Apr 2002 Physics 102 Lecture 7 2
Two slit interference Consider light passing through two slits in a screen: Constructive interference constructive (bright) fringes: destructive (dark) sinθ = mλ d, m = 012,,, 1 ( ) sinθ = m+ 4 Apr 2002 Physics 102 Lecture 7 3 2 λ d K
Single slit diffraction Interference occurs with a single slit! Each point on the wave front acts as a new source of secondary spherical waves: Huygens construction A bright spot always appears at the center. m=2 min m=1 min These rays correspond to a dark fringe. θ w λ sinθ = m 2 2 Maximum 4 Apr 2002 Physics 102 Lecture 7 4
A single slit diffraction pattern is formed with a slit of width w. The width of the slit is then doubled. Considering the central portion of the diffraction pattern... A. The angular size of the central diffraction spot doubles. B. The angular size of the pattern is reduced by two. C. The central spot stays the same size but the minima move closer to the central spot. D. More light gets through so the pattern looks the same but is brighter. 4 Apr 2002 Physics 102 Lecture 7 5
1 slit 2 slits 3 slits 4 slits 5 slits 4 Apr 2002 Physics 102 Lecture 7 6
Multislit interference (gratings) With multiple slits, the maxima occur only when constructive interference occurs from all the grating slits. Thus, the centers of lines are at the same places as with two slits sin θ = mλ d, m = 0,1,2,... but now the lines are much narrower and brighter. We call this a diffraction grating. The pattern from a single slit is still imposed on the multislit pattern. 4 Apr 2002 Physics 102 Lecture 7 7
Interference from CDs For maxima m=1 CD 4 Apr 2002 Physics 102 Lecture 7 8
A green laser (wavelength=500 nm) is reflected off a plate that contains small features. Spots are observed on a wall 10 m away. What is the approximate separation, D, of the features on the plate? A. Not enough information to tell. B. D = 15 nanometers C. D = 15 micrometers D. D = 15 millimeters 4 Apr 2002 Physics 102 Lecture 7 9
X-Ray Diffraction X-rays are electromagnetic radiation, like light, but with a wavelength of order 0.5x10-10 m (atomic radius) A crystal in an X-ray beam acts like a diffraction grating, producing Laue patterns or Bragg peaks Studying these patterns reveals the crystalline structure The structure of DNA was determined by Watson and Crick using X-ray diffraction. 4 Apr 2002 Physics 102 Lecture 7 10
A diffraction grating is illuminated with red light at normal incidence. The pattern seen on a screen behind the grating consists of three red spots, one at zero degrees (straight through) and one each at ±45. You now add green light of equal intensity, coming in the same direction as the red light. The new pattern consists of: A. Red spots at 0 and ±45. B. Green spots at 0 and ±45. C. Yellow spots at 0 and ±45. D. A yellow spot at 0, red spots at ±45, and green spots slightly farther out. E. A yellow spot at 0, red spots at ±45, and green spots slightly closer in. From Eric Mazur 4 Apr 2002 Physics 102 Lecture 7 11
Spectrum of Hg With a grating, we can study the spectra of atoms. Look to the right! Emission lines from Hg 300 400 500 nm 4 Apr 2002 Physics 102 Lecture 7 12
Imagine holding a circular disk in a beam of monochromatic light. If diffraction occurs at the edge of the disk, the center of the shadow of the disk is: From Eric Mazur A. A bright spot. B. Darker than the rest of the shadow. C. Bright are dark, depending on the distance to the screen. D. As dark as the rest of the shadow, but not as dark as without diffraction. 4 Apr 2002 Physics 102 Lecture 7 13
Shadow of a ball bearing in laser light 4 Apr 2002 Physics 102 Lecture 7 14
The Rayleigh Criterion Two point objects (e.g., headlights) can just be resolved if the first dark fringe in the diffraction pattern of one falls directly on the bright central fringe of the other. If the angle is small, then min min (NB: the angle must be expressed in radians) For the eye, D=2.5 mm, and red light, sin θ θ =122. λ/ D ~ 0.0002~0.01 deg. This is equivalent to 2 mm at 10 m distance 4 Apr 2002 Physics 102 Lecture 7 15
Interference in thin films Light reflecting off two layers of a surface can interfere with itself con/destructively. Light undergoes a half wavelength phase change when reflecting from a more optically dense medium. Constructive interference: film 2t λ λ 2 film film, + 1 = m m = 0,1,2,... 4 Apr 2002 Physics 102 Lecture 7 16
Newton s rings Here a lens projects the diverging rays onto the wall 4 Apr 2002 Physics 102 Lecture 7 17
Soap film wedge interference Gravity draws film approximately into a wedge. Slightly diverging rays require a converging lens to project on the wall. Lens inverts image. What happens to the reflected light when the film gets very thin? Puzzler: What would the film look like in transmitted light? 4 Apr 2002 Physics 102 Lecture 7 18