Physics 52 - Heat and Optics Dr. Joseph F. Becker Physics Department San Jose State University © 2005 J. F. Becker

Chapter 36 Diffraction © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

Geometric optics predicts that a straight edge should give a shadow with a sharp boundary. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

(a) Geometric shadow of a horizontal slit. (b) Diffraction pattern of a horizontal slit actually observed. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics INCORRECTCORRECT

Diffraction from a single rectangular slit. (a) Huygen’s Principle. (b) Fresnel (near field) diffraction. (c) Fraunhofer (parallel rays) diffraction. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

(a) Side view of a horizontal slit of width a. (b) Enlarged view of half the slit. The ray from the middle of the slit travels a distance a /2 sin  farther to the point P than does the ray from the top edge of the slit. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

Phasor diagrams used to find the amplitude of the E field in single-slit diffraction. (a) All phasors are in phase. (b) Each phasor differs in phase slightly from the preceding one. (c) Limit reached when the slit is subdivided into infinitely many strips. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

Intensity distribution for a diffraction from a single slit. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

(a) When the slit width a is less than or equal to the wavelength, the central maximum is spread out. (b), (c) The angular width of the central maximum decreases when the ratio of a / is increased. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

(a) Single-slit pattern slit of w = a. (b) Double-slit interference pattern. (c) Calculated pattern for curve in b. Intensity as function of  is shown in red. <<< narrow separation d = 4a © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

In multiple-slit diffraction, rays = n from every slit arrive in phase if the path difference between adjacent slits is a whole number of wavelengths: n = d sin  © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

Phasor diagrams for light passing through 8 narrow slits. Intensity maxima occur when the phase difference  = 0, 2 , 4 , … There are 7 minima. Phasor diagrams for: (a)  =  (b)  =  (c)  =  © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

Interference diagrams for N equally spaced very narrow slits: N = 2 slits N = 8 slits N = 16 slits © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

A portion of a transmission diffraction grating. d sin  = m m = 0, + 1, + 2, … at intensity maxima © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

A diffraction-grating spectrometer. The lenses between source and grating form a beam of parallel rays incident on the grating. The beam is diffracted into various orders satisfying d sin  = m  where  m = 0, + 1, + 2, … © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

GRATING SPECTROGRAPH light © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

X-ray diffraction by a crystal. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

Model of the arrangement of the ions in a crystal of sodium chloride. Na in black, Cl in red. The spacing of adjacent atoms is nm. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

(a) Scattering of waves from a rectangular array. (b) Constructive interference occurs for waves scattered at angles such that a cos  a = a cos  r. (c) Interference from adjacent rows is also constructive when path difference is 2d sin  = m. (Note  =  a =  r ) © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

A cubic crystal and two different families of crystal planes. The spacing of the planes (a) is d = a (2) -1/2 (b) is d = a (3) -1/2 There is another set of planes parallel to the cube faces with spacing a. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

Diffraction pattern aperture diameter = D © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

(a) A hologram is the record on film of the interference pattern formed with light from a coherent source and scattered light from the object. (b) Images are formed when light is projected thru the hologram. The observer sees a virtual image formed behind the hologram. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

(a) Constructive interference of the plane and spherical waves occurs in the plane of the film at every point Q for which distance b m > b o by m. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

(b) When a plane wave strikes a transparent positive print of the developed film, the diffracted wave consists of a wave converging to P’ and then diverging again, and a diverging wave that appears to originate at P. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

HOLOGRAMS – How they are made and viewed. Light emitted by an object contains the complete information on it’s size and shape. This information is stored in the variation of intensity and phase of the EM radiation,i.e., the light from the object. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

A light wave diffracted from an object interferes with a reference wave producing a diffraction pattern on the photographic film. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

When the photographic image is viewed with the reconstruction beam (same as ref. beam) a 3-dim. virtual image of the object is observed. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

Two light sources a and b produce images at c that are just resolved according to Rayleigh’s criteria. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

Review © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics