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Chapter 36: Diffraction and Polarization

Chapter 36: Diffraction and Polarization. Diffraction Single-slit Double-slit Limit on resolution Diffraction grating Polarization. Diffraction. New Topic. Diffraction pattern. . Diffraction. What if we shined coherent light through a single slit?. .

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Chapter 36: Diffraction and Polarization

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  1. Chapter 36: Diffraction and Polarization • Diffraction • Single-slit • Double-slit • Limit on resolution • Diffraction grating • Polarization

  2. Diffraction New Topic

  3. Diffraction pattern  Diffraction What if we shined coherent light through a single slit?  But instead you would see many lines on the wall: (show movie 23_7.wmv)

  4. Single-slit diffraction • Light falls straight through the slit • this forms a central bright line on the screen • Now we look at light falling through at angle q such that the top and bottom waves are one wavelength l apart. • This center wave is exactly half a wavelength l / 2 out of phase with this bottom wave this gives destructive interference

  5. The angle at which one finds the first minimum: sin  =  / a Equation for all minima: a sin = m Single-slit diffraction • Eventually we get following pattern:

  6. Example 36-1: Single-slit Diffraction • Light of wavelength 750 nm passes through a slit 1 m wide. • How wide is the central maximum on a screen 20 cm away?

  7. RESPONDEX • Wireless Interactive Classroom Y N U 2 B 3 C 1 A 5 4 6 E D 8 9 7 All Done 0 Control screen Slide with slit ConcepTest 7(Pre) Diffraction (1) narrow the slit (2) widen the slit (3) enlarge the screen (4) close off the slit • The diffraction pattern below arises from a single slit. If we would like to sharpen the pattern, i.e. make the central bright spot narrower, what should we do to the slit width? [wavopt7a]

  8. ConcepTest 7(dis) Diffraction screen Slide with slit DISCUSSION TIME • The diffraction pattern below arises from a single slit. If we would like to sharpen the pattern, i.e. make the central bright spot narrower, what should we do to the slit width? (1) narrow the slit (2) widen the slit (3) enlarge the screen (4) close off the slit

  9. q a q ConcepTest 7(ans) Diffraction (1) narrow the slit (2) widen the slit (3) enlarge the screen (4) close off the slit • The diffraction pattern below arises from a single slit. If we would like to sharpen the pattern, i.e. make the central bright spot narrower, what should we do to the slit width? The angle at which one finds the first minimum is: The central bright spot can be narrowed by having a smaller angle, this in turn is accomplished by widening the slit. sin  =  / a

  10. RESPONDEX • Wireless Interactive Classroom Y N U 2 B 3 C 1 A 5 4 6 E D 8 9 7 All Done 0 Control ConcepTest 9(Post) Diffraction (1) darker than the rest of the shadow (2) a bright spot (3) bright or dark, depends on the wave length (4) bright or dark, depends on the distance to the screen • 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 is [wavopt9b]

  11. ConcepTest 9(ans) Diffraction (1) darker than the rest of the shadow (2) a bright spot (3) bright or dark, depends on the wave length (4) bright or dark, depends on the distance to the screen • 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 is By symmetry all the waves coming from the edge of the disk interfere constructively in the middle because they are all in phase.

  12. If laser light illuminates one slit: If another slit is opened adjacent to the first, the pattern now has an interference pattern: interference minimum diffraction minimum Diffraction + Interference Yes Wait a minute!If I have two slits, don’t we also get a diffraction pattern from each slit, in addition to the interference pattern?

  13. Intensity single-slit diffraction which has minima at double-slit interference which has maxima at Young’s double-slit experiment has both.

  14. Limits of Resolution The intensity pattern of circular opening due to diffraction is Rayleigh criterion: two objects are just resolvable if they are separated by an angle given by This is the limit of resolution on optical instruments set by the wave nature of light due to diffraction.

  15. Example 36-6: radio wave vs. visible light • What is the theoretical minimum angular separation of two stars that can just be resolved by • a 200-in optical telescope? • a 300-m radio telescope? • Assume =550 nm for visible light and =4 cm for radio wave. The human eye can resolve objects whose angular separation is about 5x10-4 radians at best. This corresponds to objects separated by 1 cm at a distance of 20 m, or 0.1 mm at the near point of 25 cm.

  16. Similar to the 2-slit situation, but peaks are much narrower. Diffraction Grating • A large number of equally spaced slits (up to 10,000 !) is called a diffraction grating • useful for measuring wavelengths • how does the interference pattern look like? Principal maxima

  17. Spectrum Produced by Diffraction Grating 400 nm and 700 nm White light

  18. Example 36-7: diffraction grating The separation between slits is d=1/105 cm. • Calculate the 1st and 2nd order angles for light of wavelength 400 nm and 700 nm if the grating contains 10,000 lines per cm. 1st order m=1 2nd order m=2 So 2nd order for 700 nm does not exist. Nor do higher orders.

  19. Polarization New Topic

  20. polarized light unpolarized light E field oscillates in one direction millions of electrons E field oscillates in all directions 1 electron 3-D view: 3-D view: Polarization The E field in an EM wave is perpendicular to the direction of travel. But there are many possible orientations for the E field! In polarized light, all of the electric fields in the wave oscillate in the same direction

  21. E field of wave Wave passes through Wave absorbed long thin molecules (light) wires (radio waves) E field of wave polarized unpolarized polaroid Polarization by Absorption 1) scattering Three ways to polarize light 2) reflection 3) absorption Polarization by absorption: Vertical components of wave are absorbed by antenna Horizontal components pass through

  22. Intensity of the outgoing polarized light:I = I0 cos2 q How much light gets through? E field: Eo Intensity: Io E field: ? Intensity: ?

  23. Second polaroid is oriented perpendicular to the first one, so no light can pass through it. Polarization • First polaroid allows only one orientation of the electric field to pass, thus polarizing the light. No light

  24. Polarization by Reflection Brewster’s Angle: reflected light is totally plane-polarized parallel to the surface.

  25. 1 2 RESPONDEX • Wireless Interactive Classroom 3 Y N U 2 B 3 C 1 A 5 4 6 E D 8 9 7 All Done 0 Control (1) 1 (2) 2 (3) 3 (4) none of them (5) all of them ConcepTest 14(post) Polarization • If unpolarized light is incident from the left, at which of the points will there be some light? [wavop14b]

  26. 1 2 3 (1) 1 (2) 2 (3) 3 (4) none of them (5) all of them ConcepTest 14(ans) Polarization • If unpolarized light is incident from the left, at which of the points will there be some light?

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