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3 where s = f L (Equation 2.1) s = speed at which radiant energy travels (meters/sec or feet/sec) f = frequency (cycles/sec, or Hertz) L = wavelength (in meters or feet) A wave also has an amplitude, which is the maximum height or displacement of the crest of the wave shown in Figure 2.3 above or below its midpoint. Figure 2.3 Wavelength and Amplitude Displacement Wave Length Wave Length Amplitude Distance The crest of the longer wavelength of the two waves shown in Figure 2.2 travels past a given point less frequently during a specified period of time than the crest of the shorter wavelength wave. Therefore, the longer wavelength wave has the lower frequency and the shorter wavelength wave has the higher frequency, as shown in Figure 2.3. The horizontal axis of Figure 2.4 is the time measured at any given point on the horizontal axis of Figure 2.3. Figure 2.4 Wave Frequency and Period Displacement Wave Period Wave Period Amplitude Time Lower Frequency Wave Higher Frequency Wave The time that it takes for a wave to go through one complete cycle is called the period of the wave. The shorter the period, the more cycles the wave completes in a 17

4 given amount of time, and thus the higher its frequency. This can be expressed by the relation given by Equation 2.2. frequency = 1/ period (Equation 2.2) Since the period of a wave is expressed in seconds, the frequency of the wave is expressed in 1/seconds, to which we assign the name Hertz (Hz). All electromagnetic radiation, regardless of its source, is characterized by a frequency associated with the source and with the radiation. The wave model can describe electromagnetic radiation as sine waves of a given wavelength and frequency. Regardless of their wavelength and frequency, all waves of electromagnetic radiation travel at the same speed in a vacuum, 3 x 10 8 meters per second, the speed of light. However, light travels at different speeds in different materials. When light enters a transparent material, the speed of the wave changes and the light beam is refracted, or bent, as shown in Figure 2.5 Figure 2.5 Refracted Light Air Water The ratio of the speed of light in a vacuum to the speed of light in a material is called the index of refraction. The index of refraction is a measure of the amount that a light beam is bent as it passes from one medium to another medium. Equation 2.3 expresses the index of refraction as a ratio. Because an index of refraction is the ratio of two quantities of the same kind, there are no units associated with an index of refraction. n = speed of light in a vacuum speed of light in material (Equation 2.3) The speed of light in a vacuum is always 3 x 10 8 m/s. A beam of white light is made up of light with many frequencies. The speed of each frequency of light is different when it travels through a medium. Thus, red light bends (refracts) less than blue light. When calculating the index of refraction using Equation 2.3, it is the average speed of the light in the material that is used. Table 2.1 gives the average indices of refraction for some common materials. 18

5 Table 2.1 Average Indices of Refraction Medium Index of Refraction Medium Index of Refraction Vacuum Glass 1.52 Air Plexiglas 1.51 Diamond 2.42 Water 1.33 (Example 2.1) Light travels in a diamond at a speed of 1.24 x 10 8 meters/second. What is the index of refraction of light in a diamond? n = speed of light in vacuum speed of light in diamond = 3 x x 10 m/s 8 m/s = 2.42 As discussed earlier, electromagnetic waves are unique in that they can travel through a vacuum, and all do so with the same speed (3 x 10 8 m/s). Other types of waves, such as sound waves, must travel through a medium such as air or water. Sound waves travel at varying speeds, for example at 343 m/s in dry air at room temperature and at 1,440 m/s in water. The amount that light is refracted depends on the frequency of the light wave. When light passes through a prism, the waves with the highest frequency are refracted more than waves of lower frequency. This difference in refraction separates the light into a rainbow of colors. Figure 2.6 A Prism Refracts Light White light Prism Red (n=1.515) Yellow (n=1.517) Violet (n=1.525) The difference between the speed of red light and violet light is greatest for materials with the largest index of refraction. For this reason, a well-cut diamond is very effective in breaking light up into colors. The best cut for this purpose is known as a brilliant cut. 2.3 The Electromagnetic Spectrum All electromagnetic waves are the same, though they may differ in wavelength and frequency. The electromagnetic spectrum can be divided into regions according to 19

10 E.2 Which of the following does NOT make use of wave motion? a) A bowling ball strikes a bowling pin. b) A radio plays music transmitted from a radio station. c) A microwave oven heats a slice of pizza. d) Jane is reading by the light of an incandescent lamp. e) A tennis ball floating on the river bobs up and down as a boat passes by. E.3 Estimate the wavelength of a 1500 Hz sound wave. What would be the wavelength of an electromagnetic wave of the same frequency? a) 0.23 m; 5 x 10-6 m b) 0.23 m; 2 x 10 5 m c) 4.4 m; 5 x 10-6 m d) 4.4 m; 2 x 10 5 m e) 8.8 m; 6.2 x 10 5 m E.4 The index of refraction of a piece of glass is 1.5. What is the speed of the photons of light in this glass? a) 2 x 10 8 m/s b) 3 x 10 8 m/s c) 4.5 x 10 8 m/s d) The speed depends on the period of the electromagnetic wave. e) The speed depends on the frequency of the wave. E.5 Which of the following sequences has the various regions of the electromagnetic spectrum arranged in order in increasing wavelength? a) infrared, visual, ultraviolet, gamma ray b) radio, infrared, ultraviolet c) ultraviolet, visual, microwave, radio d) X-ray, visual, microwave, infrared e) gamma ray, X-ray, microwave, visual E.6 In a vacuum, microwaves travel waves of visible light. a) faster than b) slower than c) at the same speed as 24

11 E.7 Which of the following statements about the microwaves used in microwave ovens is not correct? a) Microwaves are electromagnetic radiation. b) Microwaves are the same wavelength as waves used in radio broadcasting. c) Microwaves have wavelengths longer than those of visible light. d) Microwaves heat food by the conversion of radiant energy into thermal energy. e) All of the statements are correct. E.8 How many photons of wavelength 6 x 10 5 meters are required to produce electromagnetic radiation with 3.32 x joules of energy? a) 1 x 10 6 photons b) 1 x 10 3 photons c) 1 x 10 6 photons d) 5 x 10 6 photons e) 1 x photons Period 2 Review Questions R.1 What is the source of radiant energy? R.2 How are the forms of radiant energy associated with the electromagnetic spectrum similar? How do they differ? R.3 Give an example of each of the forms of radiant energy. R.4 How can you find the energy of a photon of radiant energy? R.5 Compare the speed of sound to the speed of light in air. What is the ratio of the speed of sound to the speed of light? 25

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