• Interference can be used to measure the wavelength of a monochromatic light (see the example in Section 3.2.3).
• A common example of the applications of interference involves the interference of radio wave signals which occur at the antenna of a home when radio waves from a very distant transmitting station take two different paths from the station to the home. This is relatively common for homes located near mountain cliffs. In such an instance, waves which travel directly from the transmitting station to the antenna interfere with other waves which reflect off the mountain cliffs behind the home and travel back to the antenna, as shown in Figure 47.
Figure 46 Examples of continuous spectrum, line spectrum, and absorption spectrum.
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In this case, waves are taking two different paths from the source to the antenna - a direct path and a reflected path. Clearly, each path is represented by a different distance traveled from the source to the home, with the reflected pathway corresponding to the longer distance of the two. If the home is located at some distance d from the mountain cliffs, then the waves which take the reflected path to the home will be traveling an extra distance given by the expression 2d.
The 2 in this expression is due to the fact that the waves taking the reflected path must travel past the antenna to the cliffs (a distance d) and then back to the antenna from the cliff (a second distance d).
Thus, the path difference of 2d results in destructive interference whenever it is equal to odd multiple of half wavelengths.
Since radio stations transmit their signals at specific and known frequencies, the wavelengths of these ‘light’ waves can be determined by relating them to the transmitted frequencies and the light speed in vacuum (3 x 108 m/s).
♦ Creating holography
• Holography is a method (technique) of producing a three-dimensional image of an object by recording on a photographic plate or film the pattern of interference formed by a split laser beam and then illuminating the pattern either with a laser or with ordinary light.
• The technique is widely used as a method for optical image formation and, in addition, has been successfully used with acoustical (sound) and radio waves.
• The technique is accomplished by recording the pattern of interference between the wave emanating from the object of interest and a known reference wave, as shown in Figure 48a. In general, the object wave is generated by illuminating the (possibly three-dimensional) subject of interest with a highly coherent beam of light, such as one supplied by a laser source. The waves reflected from the object strike a light-sensitive recording medium, such as photographic film or plate.
Simultaneously a portion of the light is allowed to bypass the object and is sent directly to the recording plate, typically by means of a mirror placed next to the object. Thus incident on the recording medium is the sum of the light wave from the object and a mutually coherent reference wave.
Figure 47 An example of radio wave interference.
Physic 1 Module 3: Optics and waves 28 .
The photographic recording obtained is known as a hologram (meaning a “total recording”); this record generally bears no resemblance to the original object, but rather is a collection of many fine fringes which appear in rather irregular patterns. Nonetheless, when this photographic transparency is illuminated by coherent light, one of the transmitted wave
components is an exact duplication of the original object wave, as shown in Figure 48b. This wave component therefore appears to originate from the object (although the object has long since been removed) and accordingly generates a virtual image of it, which appears to an observer to exist in three-dimensional space behind the transparency. The image is truly three- dimensional in the sense that the observer's eyes must refocus to examine foreground and background, and indeed can “look behind” objects in the foreground simply by moving his or her head laterally.
3.4.2 Applications of diffraction
♦ Diffraction gratings (see Section 3.3.3)
♦ Limiting of resolution of an optical instrument
• The ability of optical instrument such as a microscope to distinguish between closely spaced objects is limited because of the wave nature of light.
• Consider light waves from different objects far from a narrow slit, and these objects can be considered two noncoherent point sources S1 and S2. If no diffraction occurred, two distinct bright spots (or images) would be observed on the viewing screen. However, because of diffraction, each source is imaged as a bright central region flanked by weaker bright and dark fringes. What is observed on the screen is the sum of two diffraction patterns: one from S1 and the other from S2.
• If the two sources are far enough apart to keep their central maxima from overlapping, their images can be distinguished and are said to be resolved; as a result, the observer can see S1 and S2 distinguishably.
• If the sources are close together, however, the two central maxima overlap, and the images are not resolved; as a result the observer cannot see S1 and S2 distinguishably.
Figure 48b Obtaining images from a hologram.
Figure 48a Recording a hologram.
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Figure 49 Depicting the photoelectric effect.
• The light diffraction thus imposes a limiting resolution of any optical instrument.