11: Physical Optics
The most certain indication of a wave is interference. This wave characteristic is most prominent when the wave interacts with an object that is not large compared with the wavelength. Interference is observed for water waves, sound waves, light waves, and, in fact, all types of waves.
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- 11.2: Wave Interference
- Superposition is the combination of two waves at the same location. Constructive interference occurs from the superposition of two identical waves that are in phase. Destructive interference occurs from the superposition of two identical waves that are 180° out of phase. The wave that results from the superposition of two sine waves that differ only by a phase shift is a wave with an amplitude that depends on the value of the phase difference.
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- 11.4: Polarization
- Polarization is the attribute that a wave’s oscillations have a definite direction relative to the direction of propagation of the wave. (This is not the same type of polarization as that discussed for the separation of charges.) Waves having such a direction are said to be polarized. For an EM wave, we define the direction of polarization to be the direction parallel to the electric field. Thus we can think of the electric field arrows as showing the direction of polarization.
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- 11.5: Young's Double-Slit Interference
- Young’s double-slit experiment gave definitive proof of the wave character of light. An interference pattern is obtained by the superposition of light from two slits. When light passes through narrow slits, the slits act as sources of coherent waves and light spreads out as semicircular waves. Pure constructive interference occurs where the waves are crest to crest or trough to trough. Pure destructive interference occurs where they are crest to trough.
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- 11.6: Mathematics of Interference
- In double-slit diffraction, constructive interference occurs when d sin θ = mλ (for m=0,±1,±2,±3…), where d is the distance between the slits, θ is the angle relative to the incident direction, and m is the order of the interference. Destructive interference occurs when \(d \space sin \space \theta = (m + \frac{1}{2}) \lambda\), for m = 0,±1,±2,±3,…
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- 11.8: Double-Slit Diffraction
- With real slits with finite widths, the effects of interference and diffraction operate simultaneously to form a complicated intensity pattern. Relative intensities of interference fringes within a diffraction pattern can be determined. Missing orders occur when an interference maximum and a diffraction minimum are located together.
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- 11.9: Multiple-Slit Interference
- Analyzing the interference of light passing through two slits lays out the theoretical framework of interference and gives us a historical insight into Thomas Young’s experiments. Much of the modern-day application of slit interference uses not just two slits but many, approaching infinity for practical purposes. We start the analysis of multiple-slit interference by taking the results from our analysis of the double slit (N = 2) and extending it to configurations with numbers of slits.
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- 11.10: Diffraction Gratings
- A diffraction grating consists of a large number of evenly spaced parallel slits that produce an interference pattern similar to but sharper than that of a double slit. Constructive interference occurs when \(d \space sin \space \theta = m \lambda\) form = 0, ± 1, ±2,..., where d is the distance between the slits, θ is the angle relative to the incident direction, and m is the order of the interference.
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- 11.11: Huygens's Principle - Diffraction
- An accurate technique for determining how and where waves propagate is given by Huygens’s principle: Every point on a wavefront is a source of wavelets that spread out in the forward direction at the same speed as the wave itself. The new wavefront is a line tangent to all of the wavelets. Diffraction is the bending of a wave around the edges of an opening or other obstacle.
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- 11.12: Circular Apertures and Resolution
- Light diffracts as it moves through space, bending around obstacles, interfering constructively and destructively. This can be used as a spectroscopic tool—a diffraction grating disperses light according to wavelength, for example, and is used to produce spectra—but diffraction also limits the detail we can obtain in images.Diffraction limits the resolution in many situations. The acuity of our vision is limited because light passes through the pupil, which is the circular aperture of the eye.
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- 11.13: Interference in Thin Films
- When light reflects from a medium having an index of refraction greater than that of the medium in which it is traveling, a 180° phase change (or a λ/2 shift) occurs. Thin-film interference occurs between the light reflected from the top and bottom surfaces of a film. In addition to the path length difference, there can be a phase change.
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- 11.14: Thin Film Interference
- The bright colors seen in an oil slick floating on water or in a sunlit soap bubble are caused by interference. The brightest colors are those that interfere constructively. This interference is between light reflected from different surfaces of a thin film; this effect is known as thin film interference. Interference effects are most prominent when light interacts with something having a size similar to its wavelength. A thin film is one having a thickness smaller than a few times the wavelengt
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- 11.15: X-Ray Diffraction
- Since X-ray photons are very energetic, they have relatively short wavelengths. Thus, typical X-ray photons act like rays when they encounter macroscopic objects, like teeth, and produce sharp shadows. However, since atoms are on the order of 0.1 nm in size, X-rays can be used to detect the location, shape, and size of atoms and molecules. The process is called X-ray diffraction, and it involves the interference of X-rays to produce patterns.
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- 11.16: Holography
- A hologram is a true three-dimensional image recorded on film by lasers. Holograms are used for amusement; decoration on novelty items and magazine covers; security on credit cards and driver’s licenses (a laser and other equipment are needed to reproduce them); and for serious three-dimensional information storage. You can see that a hologram is a true three-dimensional image because objects change relative position in the image when viewed from different angles.
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- 11.17: The Michelson Interferometer
- The Michelson interferometer (invented by the American physicist Albert A. Michelson, 1852–1931) is a precision instrument that produces interference fringes by splitting a light beam into two parts and then recombining them after they have traveled different optical paths.