Electromagnetic Waves A.K.A. Light When Thomas Edison worked late into the night on the electric light, he had to do it by gas lamp or candle. I'm sure it made the work seem that much more urgent. George Carlin 1
Electromagnetic Waves Electromagnetic waves are produced by the motion of electrically charged particles. These waves are also called "electromagnetic radiation" because they consist of two components, one electrical and one magnetic, and they radiate from electrically charged particles. They travel through empty space as well as through air and other substances. 2
Electromagnetic Waves Scientists have observed that electromagnetic radiation has a dual "personality." Besides acting like waves, it acts like a stream of particles (called "photons") that have no mass. The photons with the highest energy correspond to the shortest wavelengths. 3
How Physicists Represent Electromagnetic Waves E represents the Electric Field and B represents the Magnetic Field. 4
The Electromagnetic Spectrum 5
Linear Propagation of Light The observation that light travels in straight lines is such a fundamental property that it has been given the status of a principle. The Principle of Linear Propagation of Light leads to the very useful Ray Model of light. A light ray is an imaginary arrow that points in the direction of propagation of light. Just like matter waves, light rays are always perpendicular to the wavefronts (as is shown below). 6
The Law of Reflection The angle of incidence (θ i ) will equal the angle of reflection (θ r ), and the incident light ray, the reflected light ray, and the normal to the surface all like in the same plane. 7
Regular and Diffuse Reflection Why can you see yourself in mirror but not in a piece of paper? The mirror is much smoother than the piece of paper. If you magnify the surface of a mirror several hundred times it still appears smooth, however, do the same to a piece of paper and you will find its surface to be quite irregular. 8
Regular Reflection When a set of parallel light rays hit a mirror surface the reflected rays are also parallel to one another. This is called regular (or specular) reflection. 9
Diffuse Reflection If, however, each of the light rays reflects off in a different direction, as in the figure below, it is called diffuse reflection. 10
Properties of Plane Mirrors 1. The image appears to be as far behind the mirror as the object is in front of it. 11
Properties of Plane Mirrors 2. The image is neither enlarged nor reduced. 12
Properties of Plane Mirrors 3. The image is virtual, that is, the image only appears to be formed by the convergence of rays of light. 13
Properties of Plane Mirrors 4. The image has been laterally inverted, that is, right and left appear to be switched. 14
The Speed of Light The difficulty involved in measuring the speed of light led many scientists to believe that it traveled instantaneously. In 1905 at Mount Wilson, California, Albert A. Michelson accurately measured the speed of light using a few mirrors and some basic equations. Michelson s work gave Albert Einstein the foundation on which to build his famous Theory of Relativity. The enclosure for the launch/return equipment of the Michelson speed of light experiment. 15
Michelson s Experiment Michelson set up the apparatus shown below on Mount Wilson and positioned a mirror 35 km away. A light source reflected off one side of a rotating eight sided mirror, then off the distant mirror, and finally off the viewing mirror. 16
Michelson s Experiment By determining the exact rate of rotation that gave a reflection and combining it with the distance the light traveled, Michelson calculated the speed of light to be 2.997 10 8 m/s. This is amazingly close to the currently accepted value of 2.99792458 10 8 m/s. For our purposes the speed of light will be taken as the constant c where c = 3.00 10 8 m/s 17
Faster Than The Speed of Light While it is believed to be true that no object having mass can travel faster than the speed of light in a vacuum, particles, such as electrons, can travel faster than the speed of light in a medium such as water. When this occurs you see a blue glow called Cerenkov radiation (named after the Russian scientist who studied it) this is basically the Doppler Effect for light. 18
Cerenkov Radiation The image below shows Cerenkov radiation in the core of a nuclear reactor. When highly radioactive objects are observed under water, such as in "swimming pool" reactors and in the underwater temporary spent fuel storage areas at nuclear reactors, they are seen to be bathed in an intense blue light called Cerenkov radiation. It is caused by particles entering the water at speeds greater than the speed of light in the water. As the particles slow down to the local speed of light, they produce a cone of light roughly analogous to the bow wave of a boat which is moving through water at a speed greater than the wave speed on the surface of the water. Another analogy statement is to say that the Cerenkov cone is like a sonic boom except that it is done with light. 19
Refraction of Light 20
Refraction and Light Waves Refraction is the changing of the speed of a wave when it travels from one medium into another. Light travels as a wave, and therefore experiences refraction. When light travels from one medium into another at an angle, the difference in speed causes a change in direction of the light. 21
Example of Light Refraction 22
Index of Refraction Light will refract different amounts in different materials. The amount of refraction that occurs is proportional the speed of light in that particular material. Every material has a property that we call its Index of Refraction. 23
Index of Refraction 24
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Example: Find the speed of light in ruby. 26
Optical Density The term optically dense refers to a refractive medium in which the speed of light is low in comparison to its speed in another medium. For example the speed of light in water (n= 1.33) is 2.26 10 8 m/s, whereas the speed of light in zircon (n=1.92) is 1.56 10 8 m/s. We would therefore say zircon is more optically dense than water. 27
Snell s Observation In 1621 Willebrord Snell, a Dutch mathematician, experimentally discovered a relationship to describe refraction of light. When light travels across a boundary from one medium to another, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant the medium. That is: 28
Snell s Observation Snell also observed that when light bends towards the normal when travelling from a less optically dense material into a more optically dense material. Conversely it bends away from the normal when the setup is reversed. 29
Snell s Law Many observations and experiments revealed that Shell s constant is, in fact, the ratio of the indices of refraction for the two media. This is more commonly stated as follows 30
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Example: Light travels from air into water with an angle of incidence of 35.0 o. Find the angle of refraction. 32
Example: Light incident from ruby onto an unknown solid at 25.0 o from the normal refracts at 32.0 o from the normal. Find the index of refraction for the unknown solid. 33
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Homework: Textbook Page 400 Questions 7, 8, 9 Textbook Page 405 Questions 10, 11 35
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Even More Refraction of Light 39
Why Does Light Bend? We know from our studies of matter waves that when a wave travels from one medium to another the frequency of the wave stays the same. From the equation v = fλ we can also see that if v decreases and f stays the same then λ must also decrease. Similarly, if v increases then λ must also increase. 40
Why Does Light Bend? The figure to the right illustrates the behaviour of a light wavefront as it passes from air to water with an angle of incidence of 0 o. From the equation v = fλ we can also see that if v decreases and f stays the same then λ must also decrease. Similarly, if v were to increase then λ would also increase. 41
Why Does Light Bend? Now consider wavefronts approaching the boundary between two media at an angle.. Huygen s Principle Java Applet 42
Total Internal Reflection The incident lignt shown to the left is partially reflected and partially refracted as it leaves the Plexiglass (bottom) and enters the air (top). 43
Total Internal Reflection Eventually, we will increase θ i to the critical angle (θ c ) where θ R = 90 o exactly. If θ i > θ c then no refraction occurs and we get total internal reflection. 44
Total Internal Reflection Once we move beyond the critical angle, Total Internal Reflection occurs. 45
Conditions for Total Internal Reflection 46
Applications of Total Internal Reflection Optical Fibers 47
Applications of Total Internal Reflection Cameras, Binoculars, etc. 48
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ERR: DOMAIN 50
Homework: Textbook Page 410 Questions 12, 13, 14 Refraction Problems Handout: Questions 13 and 14 (a) 51
Air: n = 1.000 20.0 o Zircon: n = 1.92 110.0 o 35.0 o 52
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Diffraction and Interference 58
Diffraction The phenomena observed when waves are obstructed by obstacles or pass through apertures are called diffraction effects. 59
Diffraction All (two or three dimensional) waves exhibit diffraction effects but the magnitude of these effects depends on the wavelength of the waves. Diffraction effects are most obvious when the wavelength of the incident wave is comparable to or bigger than the aperture or obstacle. 60
Interference Interference is the result of the superposition of two waves. Interference can be constructive when two waves add together and amplify each other or destructive when two waves add together and cancel each other out. 61
Interference and Path Difference Consider the two wave sources shown above. 62
Interference and Path Difference s 1 = 6λ s 2 = 8λ Path Difference s s = 2λ 63
Interference and Path Difference s 1 = 6.5λ s 2 = 7.5λ Path Difference s s = 1λ 64
Interference and Path Difference s 1 = 3.5λ s 2 = 4λ Path Difference s s = 0.5λ 65
Interference and Path Difference s 1 = 4.5λ s 2 = 6λ Path Difference s s = 1.5λ 66
Conditions for Constructive Interference Constructive interference occurs if the path difference between the two waves is an integral multiple of the wavelength. d 1 d 2 = nλ n = 0, ±1, ±2, ±3, 67
Conditions for Destructive Interference Destructive interference occurs if the path difference between the two waves is off by half a wavelength. d 1 d 2 = (n + ½)λ n = 0, ±1, ±2, ±3, 68
Thomas Young (1773 1829) At the age of 17, he developed an accurate theory on color before the discovery of cone cells in the eye. By the time he was 28 he was a professor of natural philosophy at the Royal Institute in England. He was also an Egyptologist who helped decipher the Rosetta Stone. He is credited with establishing the principle of interference of light and developed the famous double slit experiment we are about to study. 69
Young s Double Slit Experiment With a monochromatic light source and the setup shown to the right, Thomas Young was able to prove that light waves interfere with each other. 70
The double slits acted like two distinct sources which he was able to place much closer together than would have been possible if two separate sources were used. Young s Double Slit Experiment 71
The light passing through the initial slit acted as a point source. When the wavefront reached the double slits two parts of the same wavefront become new sources that are perfectly in phase. Young s Double Slit Experiment 72
Young s Double Slit Experiment The interference pattern becomes visible when projected onto a screen. NOTE: We call the bright spots fringes. 73
Path Difference 74
Path Difference Basic Trigonometry tells us that: sinθ = opp / hyp sinθ = P.D. / d (P.D) or P.D. = d sinθ 75
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Constructive Interference 77
Double Slit Patterns From Lasers with Different Wavelengths 78
Example 79
(1) (2) A third order fringe from 610 nm light is observed at an angle of 18 o when light falls on two narrow slits. How far apart are the slits? (3) If 720 nm light passes through two slits 0.58 mm apart what is the distance from the central maximum to the second order fringe on a screen 1.0 m away? 80
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Multiple Slit Diffraction 82
The Diffraction Grating A diffraction grating has thousands of narrow apertures. Consider a typical grating having 5000 lines/cm. The situation can be analysed in the same way as Young s two slit experiment. 83
The Diffraction Grating If distance b c is λ then waves from a and b will interfere constructively at a point in a direction perpendicular to the normal. However, if b c is λ then d e will be 2λ, f g will be 3λ and so on. Therefore, waves from hundreds of slits will interfere constructively, producing a well defined maximum of the diffraction pattern, called a diffraction image. Other maxima will occur when b c = 2λ, 3λ etc. 84
A green laser with wavelength 532 nm is shone through a diffraction grating having 5275 lines/cm onto a screen 1.5 m away. What is the distance from the central maximum to the first order maximum on the screen? 85
Ångströms The Ångström is named after the Swedish physicist Anders Jonas Ångström (1814 1874). 1 Å = 10 10 m = 0.1 nm 86
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