The Nature of Light

1. The Nature of Light • The Electromagnetic Spectrum • Polarization • Measuring the Speed of Light • The Wave Nature of Light • The Particle Nature of Light • Refractive Index Photograph of a living fetus using fiber-optic photography

2. The Electromagnetic Spectrum Electromagnetic Waves When electric charge changes its motion (I.e. vibrates back and forth, as in an electron in a transmitting ariel), it produces a changing electric field over time. Because the electric field is changing, a changing magnetic field is induced (according to Ampere’s Law) and this in turn further generates a changing electric field (according to Faraday’s Law). Thus a continually self generating wave consisting of varying electric and magnetic fields (that are in phase but perpendicular to the direction of motion) will travel through space away from the source in all directions unless constrained, by cable. This self-generating wave is called an electromagnetic wave. Think of a radio mast transmitting your favorite radio show. There are electrons within the mast that are made to oscillate back and forth by applying a alternating electrical voltage to the mast. These vibrating electrons produce the radio waves (electromagnetic waves) that are transmitted. All waves in the electromagnetic spectrum consist of varying electric and magnetic fields. But what is the difference between a radio wave and an light wave or an x-ray? Electromagnetic waves exist with an enormous range of frequencies. This continuous range of frequencies is known as the electromagnetic spectrum. The entire range of the spectrum is often broken into specific regions. The subdividing of the entire spectrum into smaller spectra is done mostly on the basis of how each region of electromagnetic waves interacts with matter.The longer wavelength, lower frequency regions are located on the far left of the spectrum and the shorter wavelength, higher frequency regions are on the far right.

3. Polarization Have you ever worn a pair of Polaroid sunglasses? If you haven’t then on your next visit to the mall try on a pair and look at the shiny floor. What you should notice is that the sunglasses have somehow cut out all the “glare”, which is the light reflected off the floor. Fishermen like to wear sunglasses made from polarizing material (Polaroids) because they cut out the glare from the surface of the water and therefore help them locate likely fish holding areas of the river. So how does this amazing optical material work? First you must realize that electromagnetic waves are produced by vibrating electrons and that these electrons are restricted in their motion to a plane of vibration. This means that the EM wave produced by one electron is a transverse wave that moves in a plane. See diagram a. We call this plane polarized. A vertically vibrating electron emits light that is vertically polarized while a horizontally vibrating electron emits light that is horizontally polarized. See diagram b. For a common light source such as an incandescent light or the sun, the light is not polarized because the vibrating electrons that produce the light vibrate in all directions. However when the light is reflected off say the floor, the light becomes polarized in the horizontal direction. The floor effectively stops the vertical component of the wave. Glare is thus horizontally polarized. The polarizing axis of Polaroid sunglasses is vertical so that only the vertical component of EM waves gets through the material. Glare from a horizontal surface therefore cannot get through the polarizer and is thus eliminated. Diagram a. Vertically plane polarized wave emitted by a vibrating electron Diagram b. Vertical and horizontal polarization Diagram demonstrating how a Polaroid filter works. For two filters placed over each other with their axes aligned in the vertical direction, light polarized in the vertical direction can get through. If however the filters are “crossed” with their axes perpendicular to each other, light polarized in the vertical plane by the first filter cannot pass through the second filter (which only passes light having a EM component in the horizontal plane).

4. The Visible Light Spectrum Though electromagnetic waves exist in a vast range of wavelengths, our eyes are sensitive to only a very narrow band. Since this narrow band of wavelengths is the means by which humans see, we refer to it as the visible light spectrum. Normally when we use the term "light," we are referring to a type of electromagnetic wave which stimulates the retina of our eyes. In this sense, we are referring to visible light, a small spectrum of the range of frequencies of electromagnetic radiation. This visible light region consists of a spectrum of wavelengths, which range from approximately 700 nanometers (abbreviated nm) to approximately 400 nm; that would be 7 x 10-7 m to 4 x 10-7 m. This narrow band of visible light is affectionately known as ROYGBIV. The Speed of Light Early experiments to measure the speed of light failed because it was so high. Experimenters who tried to measure how how it took light to travel to a mirror placed on a distant hillside and back (Galileo) only managed to measure their own reaction time. Incidentally, it was mirrors placed on the moon by the first “manned landing” missions that later led to increased accuracy about the speed of light. Roemer’s Method So how did early physicists measure the speed of light? The first demonstration that light travels at a finite speed was supplied by the Dutch astronomer Olaus Roemer about 1675. Roemer made very careful measurements of the periods of Jupter’s moons. The innermost moon, Io, is visible through a small telescope and was measured to revolve around Jupiter in 42.5 hours. Io disappears periodically into Jupiter’s shadow, so this period could be measured with great precision. Roemer was puzzled to find an irregularity in the measurements of Io’s observed period. He found that while the earth is moving away from Jupiter, say from position B to C in the diagram opposite, the measured periods of Io were all somewhat longer than average. When the earth was moving toward Jupiter, say from position E to F, the measured periods were shorter than average. Roemer estimated that the cumulative discrepancy between positions A and D amounted to about 22 minutes. (This time is known today to be about 17 minutes or 1000s). That is when the earth was at position D, Io would pass into Jupiter’s shadow 22 minutes late compared with observations at position A.

5. The Dutch physicist Christian Huygens correctly interpreted this discrepancy. When the earth was further away from Jupiter, it was the light that was late, not the moon. Io passed into Jupiter’s shadow at the predicted time, but the light carrying the message did not reach Roemer until it had traveled the extra distance across the diameter of the earth’s orbit. speed of light = extra distance traveled = 300 000 000 km = 300 000 km /s extra time measured 1000 s Michelson’s Technique The most famous experiment measuring the speed of light was performed by the American physicist Albert Michelson in 1880. The diagram below shows that he rotated an octagonal mirror at such a rate so that light from a source would hit a mirror, travel to a distant mirror and be reflected back. If the mirror was rotated such that the time taken for the light to go to the distant mirror and back was the same time for the mirror to turn on-eighth of a rotation, the light would be reflected into the eyepiece. If too slow or too fast it wouldn’t enter the eyepiece. Finding the total distance traveled by the light (from surveyed charts), and the time to travel, (judged accurately from the rotation rate of the mirror), Michelson could determine the speed of light. Michelson’s experimental value for the speed of light was 299 920 km/s. which we round to 300 000 km/s. Michelson received the 1907 Nobel Prize in physics for this experiment. He was the first American scientist to receive this prize. Light is so fast that if a beam of light could travel around the earth, it would make 7.5 trips in one second. Light takes 8 minutes to travel from the sun to earth, and 4 years from the next nearest star Alpha Centauri. The distance light travels in a year is called a light year.

6. The Wave Nature of Light A Scottish physicist James Clerk Maxwell (1831 - 1879) produced a single theory of electromagnetism that predicted that light was an electromagnetic wave that traveled at the same speed in a vacuum as other electromagnetic waves regardless of its wavelength. Other scientists had previously showed that light exhibited properties of a wave. For example, Thomas Young showed in 1801 that light from two coherent sources will interfere. But Maxwell proved that light of all wavelengths travel at the same speed in a vacuum and that its speed is the same as all other electromagnetic waves. We can therefore say that: Speed of a EM Wave = # Waves per second • length of a Wave v f  For light in a vacuum we call its speed c = 3 x 108 m/s. We can therefore write: c = f  or f = c /  or  = c / f The Particle Nature of light Before being shown that it was waves, scientists believed it was made of particles. Today it is known to be made of particles called photons and it is also waves. The energy of a photon is proportional to its frequency and all the photons of a given frequency have the same amount of energy. We can say: Energy of a Photon = Planck’s Constant • # Waves per second E h f The constant h is known as Planck’s constant and is the same h used in describing angular momentum and spin on the atomic level. Its SI value is 6.63 x 10-34 Js. Sample Practice Problem What is a) the frequency of a 450 nm light wave? b) how much energy would each photon have and c) what color is this wavelength? We know that:  = 450 x 10-9 m, c = 3 x 108 m/s and h = 6.63 x 10-34 Js Therefore f = c /  = 3 x 108 m/s / 450 x 10-9 m = 6.67 x 1014 s-1 (Hz) E = h • f = 6.63 x 10-34 Js • 6.67 x 1014s-1 = 4.42 x 10-19 J The light has a small wavelength in the blue part of the spectrum

7. Electron-Volt Light particles have small amounts of energy which can be expressed as electron-volts. 1 eV = 1.6 x 10-19 J How much energy does a blue light particle carry in eV’s? Eblue = 4.42 x 10-19 J ( 1eV ) 1.6 x 10-19 J Eblue = 2.76 eV Photoelectric Effect This effect made famous by Einstein in 1905 is used today in electronic sensory equipment from burglar alarms and garage door openers to smoke detectors and light meters (photography). When a light photon with enough energy strikes the thin metal sheet an electron is ejected from the surface of the metal and attracted towards the positive plate. The electron then moves through the wires towards the positive side of the battery. As it moves through the ammeter (A), it causes the needle to move, thus signifying an electric current. Note: another electron will also move from the negative side of the battery through the wire to the metal plate to fill the hole vacated by the ejected electron. If light was a wave, then as the intensity of light (brightness) is increased the number of ejected electrons would increase but the frequency of light would not be a factor in getting the ejected electrons to move to the plate. A + Photon + Electron ejected - Thin metal plate

8. Einstein found out that although increasing the light intensity did increase the current, the ability of an electron to leave the surface of the metal depended on the frequency of light. He showed that the number of ejected electrons depended on the intensity of light (which was proportional to the number of photons), but the kinetic energy of the emitted electrons depend on the frequency of the light source (predicted by photon theory, E = h f)) and not the intensity of the light source (predicted by wave theory). Kinetic Energy of Electron If light is a particle (found experimentally) If light is a wave (not found experimentally) fo frequency (Hz) The graph above (solid line) shows that if light acts as a particle (photon) the kinetic energy of the electrons leaving the surface of the metal will go up in proportion to the frequency. A few photons of blue or violet light can eject a few electrons, but hordes or red or orange photons cannot eject a single electron. Only high-frequency photons have the concentrated energy needed to pull loose an electron. Einstein’s explanation for the photoelectric effect was verified 11 years later by American physicist Robert Millikan. Every aspect of Einstein’s interpretation of the photoelectric effect was confirmed, including the direct proportionality of the photon energy to frequency. It was for this that Einstein received his first Nobel Prize in Physics.

9. The Speed of Light in Transparent Materials and Refractive Index Electrons in glass have a natural vibration frequency in the ultraviolet range. When ultraviolet light shines on glass, resonance occurs as the wave builds and maintains a large vibration between the electron and the atomic nucleus, just as a large vibration is built when pushing someone at the resonant frequency on a swing. The energy received by the atom can be passed on to neighboring atoms by collisions, or reemitted as light. If ultraviolet light interacts with an atom that has the same natural frequency, the vibration amplitude of its electrons becomes unusually large. The atom typically holds on to its energy for quite a long time (about 1 million vibrations or 100 millionths of a second). During this time the atom makes many collisions with other atoms and gives up its energy in the form of heat. That’s why glass is not transparent to ultraviolet. But when the electromagnetic wave has a lower frequency than ultraviolet, as visible light does, the electrons are forced into vibration with smaller amplitudes. The atom holds the energy for less time, with less chance of collision with neighboring atoms, and less energy is transferred as heat. The energy of the vibrating electrons is reemitted as transmitted light. (see diagram below) Glass is transparent to all frequencies of visible light. The frequency of the reemitted light passed from atom to atom is identical to that of the light that produced the vibration to begin with. The main difference is a slight time delay between absorption and reemission. The time delay results in a lower average speed of light through a transparent material as shown in the diagram below. Light travels at different average speeds through different materials. In water light travels at about 75% of its speed in a vacuum, or 0.75c. In glass light travels at about 0.65c, depending on the type of glass. In a diamond light travels at only 0.40c, less than half its speed in a vacuum. When light emerges from these materials into the air, it travels at its original speed, c. The ratio of the speed of light in a vacuum to the speed v in a given material is called the index of refraction, n, of the material n = c / v Example What is the approximate index of refraction of water? nwater = c / vwater = c / (0.75 c) = 1 / 0.75 = 1.33