Presentation on theme: "Diffraction vs. Interference"— Presentation transcript:
1 Diffraction vs. Interference Both involve superposition of coherent lightCustomInterference – only a few wavesDiffraction – large number of wavesFresnel correction to Huygens Principle:Every unobstructed point of of a wavefront, at a given instant, serves as a source of spherical secondary wavelets (with the same frequency of that of the primary wave). The amplitude of the optical field is the superposition of all these wavelets (considering their amplitudes and relative phases)
2 Fraunhofer vs. FresnelFresnel – Diffraction is occurring near the aperture. a.k.a “near field diffraction”Initially the fringe pattern looks like the aperture but then the pattern changes as the distance from the aperture increases.Fraunhofer – Diffraction occurs far from the aperture. a.k.a “far field diffraction”In this region the fringe pattern remains constant, changing only in size as distance from the aperture increases.
4 Figure 38.2 Light from a small source passes by the edge of an opaque object and continues on to a screen. A diffraction pattern consisting of bright and dark fringesappears on the screen in the region above the edge of the object.Fig 38-2, p.1207
5 Single-Slit Diffraction The finite width of slits is the basis for understanding Fraunhofer diffractionAccording to Huygens’s principle, each portion of the slit acts as a source of light wavesTherefore, light from one portion of the slit can interfere with light from another portion
11 Final Exam Problem 48Light of wavelength 632 nm is incident on a single slit. The distance from the slit to a screen is 3 m. If the distance from the first minimum on one side of the center of the diffraction pattern to the first minimum on the other side is 8 mm, the width of the slit is closest to0.22 mm0.31 mm0.47 mm0.59 mm0.66 mmscreen3 m
19 Resolution, Example Pluto and its moon, Charon Left: Earth-based telescope is blurredRight: Hubble Space Telescope clearly resolves the two objects
20 Final Exam Problem 49A boat has lights on a mast that are 1 m apart. The dominant wavelength in the lights is 600 nm. The pupil in a person’s eye has an opening of 1 mm. For simplicity, we assume that the eye has a refractive index of 1. If the boat is closer, the person sees two lights on the mast. If the boat is farther away, the person sees only one light on the mast. The best value for the distance from the person to the boat is1.4 km1.2 km2.0 km1.6 km1.8 km1 m
22 Final Exam Problem 50A beam of light is incident on a diffraction grating that has 600 lines/mm. The second order maximum occurs at a distance 0.7 m from the center of a screen that is 1.0 m from the grating. The wavelength of light is closest to:478 nm613 nm574 nm589 nm542 nmgrating0.7 m1.0 m
23 Polarization “Linear” or “plane” polarization Vertically polarized Processes for accomplishing polarization:selective absorptionreflectiondouble refractionscatteringUnpolarized?Horizontally polarized
24 Polarization by Selective Absorption The most common technique for polarizing lightUses a material that transmits waves whose electric field vectors lie in the plane parallel to a certain direction and absorbs waves whose electric field vectors are perpendicular to that direction
25 Polarizing Sheets – Selective absorption Law of Malus:
27 Polarization by Double Refraction Unpolarized light splits into two plane-polarized raysThe two rays are in mutual perpendicular directionsIndicated by the dots and arrows
28 Polarization by Scattering, Rayleigh Scattering The horizontal part of the electric field vector in the incident wave causes the charges to vibrate horizontallyThe vertical part of the vector simultaneously causes them to vibrate verticallyIf the observer looks straight up, he sees light that is completely polarized in the horizontal direction
29 Final Exam Problem 37When unpolarized light is passed through two polarizing filters in succession, its intensity is decreased by 80%. The angle, q, between the transmission axis of the filters is78.5 degrees63.4 degrees26.6 degrees36.9 degrees50.8 degreesqI=0.2IoPolaroids
30 3. A screen is placed 50.0 cm from a single slit, which is illuminated with 690-nm light. If the distance between the first and third minima in the diffraction pattern is 3.00 mm, what is the width of the slit?6. Light of wavelength nm illuminates a single slit mm in width. (a) At what distance from the slit should a screen be located if the first minimum in the diffraction pattern is to be mm from the center of the principal maximum? (b) What is the width of the central maximum?18. A binary star system in the constellation Orion has an angular interstellar separation of 1.00 × 10–5 rad. If λ = 500 nm, what is the smallest diameter the telescope can have to just resolve the two stars?
31 41. Plane-polarized light is incident on a single polarizing disk with the direction of E0 parallel to the direction of the transmission axis. Through what angle should the disk be rotated so that the intensity in the transmitted beam is reduced by a factor of (a) 3.00, (b) 5.00, (c) 10.0?45. The critical angle for total internal reflection for sapphire surrounded by air is 34.4°. Calculate the polarizing angle for sapphire.