The Electromagnetic Spectrum

Transcription

1 Physics 25 Chapter 24 Dr. Alward Electromagnetic Waves Electromagnetic (EM) waves consist of traveling electric and magnetic disturbances. One source of electromagnetic waves are electric charges oscillating at some frequency. Whatever the oscillation frequency is, that is the frequency of the EM wave they produce. At any point within the wave the electric field component is perpendicular to the magnetic field component. EM waves travel through air and transparent materials with a speed that varies depending on the substance. Through air or vacuum, the speed of electromagnetic waves is 3.0 x 10 8 m/s (186,000 miles/second); this speed is called the speed of light and is symbolized as c. In other substances, such as glass and water, the speed is less than this. The Electromagnetic Spectrum The smaller the wavelength, the more harmful electro-magnetic (EM) radiation is to living things. X-rays and gamma rays have wavelengths short enough to disrupt chemical bonds, and even nuclei, which can lead to mutations of DNA, and cancer; if the intensity of gamma radiation is great enough--such as can occur near the detonation of an atomic bomb, or a hydrogen bomb-- death to living organisms can come virtually immediately. 1

2 Example A: DNA-destroying gamma radiation has wavelength comparable to the diameter of atomic nuclei: 1.0 x m. What is the frequency of gamma radiation that has this wavelength? Similar to the wave equation for sound waves, v = λf, we have for electromagnetic waves: c = λf f = c/λ f = 3.0 x 10 8 /1.0 x = 3.0 x Hz Example D: Example B: The broadcast frequency of an AM radio is 600 kilohertz. What is the wavelength? λ = c/f = 3.0 x 10 8 / 600 x 10 3 = 500 m Example C: What is the range of frequencies of green light, which occupies a portion of the visible spectrum that extends from 480 nm to 540 nm? f = 3.0 x 10 8 / 540 x 10-9 = 5.56 x Hz f = 3.0 x 10 8 / 480 x 10-9 = 6.25 x Hz Earth is about 93 million miles from the sun. If the fires of the sun were suddenly extinguished, after how many minutes would Earth be plunged into darkness? Distance: (93 x 10 6 mi) (5280 ft/mi) / (3.28 ft/m) = 1.50 x m Time = (1.50 x m)/ (3.0 x 10 8 m/s) = 499 s = 8.32 minutes 2

3 The Doppler Effect for Light If the distance between a source of light and an observer is increasing, the light frequency seen by the observer is less than the frequency of light emitted, and the corresponding observed wavelength is longer than the wavelength emitted. This increase is labeled a red shift, because the observed light wavelength is shifted toward the longer wavelength end of the visible spectrum. If the distance is decreasing, a blue shift occurs. The light source below is moving to the right. The observer at the left sees red-shifted light; the observer on the right sees blue-shifted light. v = relative speed between source and observer fo = observed frequency fs = source frequency fo = fs (1 ± v/c) If the distance between source and observer is increasing, use the negative sign. If the distance between source and observer is decreasing, as is the case when the light source is approaching the observer, use the positive sign. This situation, in which the observed frequency is higher than the broadcast frequency, is analogous to the heard frequency from an ambulance approaching a stationary listener. 3

4 Example: Red light from a galaxy is observed on Earth to have wavelength of 590 nm. Observers in the galaxy see 650 nm light. (a) What is the relative speed between the galaxy and Earth? Express your answer as a fraction of c. (b) Is the galaxy moving toward Earth, or away from Earth? Solution: (a) fo = fs (1 ± v/c) c/λo = c/λs (1 ± v/c) Divide both sides by c: 1/590 = 1/650 (1 ± v/c) The left side is larger than 1/650, so we must choose the positive sign to make the parentheses greater than 1: 1/590 = 1/650 (1 + v/c) v/c = 650/590-1 = 0.10 (b) The observed light has a smaller wavelength and higher frequency than the source light, so the galaxy is moving toward Earth, analogous to the listener hearing a higher frequency than that which is broadcast from an approaching siren. 4

5 Why are sunsets and sunrises red? Recall from our study of sound that sound waves efficiently disturb, and are disturbed by, particles that have sizes comparable to the wavelength of the sound. Sunlight consists of roughly equal parts of red, orange, yellow, blue, indigo and violet light, which, taken together, make white light. Nitrogen and oxygen molecules have sizes comparable to the wavelengths of the blue end of the visible spectrum and therefore absorb and re-radiate the shorter wavelengths more than the longer wavelengths. In passing low on the horizon at sunrise or sunset through 200 miles of the atmosphere to a viewer s eye, significant scattering of the green, blue, indigo, violet (GBIV) portion of the light occurs. As a consequence, the light on the blue end of the visible spectrum is scattered off the molecules in all directions, as shown in the figure below. Scattering of light happens far less often for the light on the longer wavelengths, red-orangeyellow (ROY), end of the spectrum. For the most part, the red, orange, and yellow wavelengths pass through the atmosphere undisturbed, and the eye, looking at the sun at sunset or sunrise, sees a reddish sun. 5

6 Why is the Sky Blue? On a cloudless day, with sunlight passing over the shoulder of the observer in the diagram below, redorange-yellow light goes straight through, but a significant amount of the blue end of the visible spectrum is scattered in all directions, including back toward the eye of the observer, who thereby sees bluish light, i.e., blue sky. ` 6

7 What Color is the Overhead Sun? Looking directly at the sun at noon in June in the Northern Hemisphere when the Sun is directly overhead is not the same as looking directly at the sun when it is about to sink below the horizon at sunset, or rise at sunrise. In the latter cases, the light from the sun has to pass through a 200-mile-long atmospheric filter that scatters the light and drains from it most of its energy; one can view the sun at sunset and sunrise for a few seconds without fear of damaging the retinas. However, the overhead sunlight at noon on a cloudless day in June is white--blindingly white, literally, because it passes through a layer of atmosphere only 40 miles thick. Some GBIV scattering does take place, but not enough to reduce the intensity to a safe viewing level. Do not look at the overhead sun on a cloudless day, even for two seconds. Also, avoid staring too long at the sun at sunset or sunrise. 7

8 Light Intensity Light intensity (I) at some point is the number of joules per second of light energy per square meter. The units of light intensity are watts per square meter (W/m 2 ). The intensity varies with the distance r from the source, and depends on the output power P of the source. The intensity at a distance r from a spherically symmetric light source is given by the equation below: I = P/4πr 2 The quantity 4πr 2 is the area of the surface of an imaginary sphere of radius r, at the center of which is the light source. The table at the right shows the dependence of intensity (I) on the distance (r) from a light bulb, whose output power is P = 60 W. For example, at a distance r = 0.10 m, I = 60 W/(4π x m 2 ) = 480 W/m 2 r (m) I (watts/m 2 ) Note the inverse square dependency of intensity on distance. For example, doubling the distance reduces the intensity to (1/2) 2 = 1/4 of the previous value. This is what happens when 19.2 W/m 2 becomes ¼ (19.2) = 4.8 W/m 2 when the distance changes from 0.50 m to 1.00 m. Increasing the distance to ten times the previous distance reduces the intensity to (1/10) 2 = 1/100 th of the previous intensity. For example, 480 W/m 2 becomes 4.8 W/m 2 when the distance increases from 0.10 m to 1.00 m. 8

9 Mixing Colors of Light Humans have trichromatic color vision, meaning that the color sensors (cones) in the retina respond more efficiently to the three colors red, green, and blue (RGB) light, than to other colors. These three colors are called the primary colors. Mixtures of any two of the primary colors of light result in colors that are called the secondary colors : magenta, yellow, cyan. Mixtures in various intensities of R, G, and B, produce various color sensations when they land on the retina. Below are the colors produced when equal intensities of the primary colors are mixed together. Keep in mind: we are mixing light waves, not paint. (Mixing paint comes later.) Memorize This Table of Colors R = Red G = Green B = Blue R+G = Yellow (Y) R+B = Magenta (M) G+B = Cyan (C) R+G+B = White (W) K = Black Example A: What intensity of red light must be added to 70 watts/m 2 of cyan light to create white light, and what will be the intensity of the light created? 70 C = 35 G + 35 B Add 35 R: 35 R + 35 G + 35 B = 105 W 105 W/m 2 of white light is created. Example B: Green light of intensity 40 watts/m 2 is mixed with magenta light whose intensity is 60 watts/m 2. What is the resulting intensity and color? Solution: 60 M = 30 R + 30 B Add 40 G: 30 R+ 30 B + (30 G +10 G) = 90 W + 10 G = 100 watts/m 2 Color: pale green, or light green. 9

10 Example: 60 W/m 2 of magenta light is mixed with 60 W/m 2 of yellow light. What single color must be added to create white light? What is the intensity of the added color? What is the intensity of the resulting white light? Colors of Objects Objects are red (in white light) because the chemical composition of the surface of the object is such that green and blue light shining on them are absorbed; only the red portion of any light shining on a red object is not absorbed; it is instead reflected to the eye of the observer. In the four examples below of light of various colors shining on a red apple, red light is reflected only if the incident light contains red, as is the case for white, magenta, and yellow light, but not cyan. 10

11 Objects that are magenta absorb only green from incident light and reflect red and blue. In the two examples below, incident light has absorbed out of it any green light that may be present, and reflects what s left: Color Filters Color filters are transparent to certain colors of light, and absorb the others. Cyan filters held up to white light will allow green and blue through, but absorb red. Yellow filters will allow red and green through, but absorb blue. Magenta filters will allow red and blue through, but absorb green. 11

12 Color Filter Exercise In each of the six situations below indicate which color is absorbed, and which gets through. The names of color filters indicate which color or colors pass through the filter, not which colors are absorbed. A yellow (RG) filter, for example, allows R and G through, but absorbs blue. 12

13 Example: A cyan filter is placed side-by-side with a yellow filter, and white light is incident on the pair. What color is transmitted through the pair? Answer: Green Mixing Paints Objects absorb certain colors, and reflect the others. Paint does the same thing. When paint of two different colors are mixed, each one of the paints absorbs a certain color from the white light shining on the mixture. The color of the resulting paint is whatever results when the absorbed colors are subtracted from white light. For example, yellow paint absorbs blue, while magenta paint absorbs green. Mixed together, the combination absorbs green and blue light from incident white light, allowing only red to be reflected: the mixture is red. Remember: we are mixing paints, not light waves. Mixing light waves is an additive process, such as when we mix red and green light waves to create yellow light. On the other hand, mixing paints is a subtractive process, such as when we mix magenta and cyan paints. The result is what you get when you subtract green and red light from incident white light, and reflect what s left (blue). 13