Various Light Phenomena & Radio Pulses PDF

# Various Light Phenomena and Hertz Produced by Radio Pulses Rainbows, sunsets and halos; a spectacular display of colors and visuals in the sky called "atmospheric optics" or light phenomena. As sunlight (or moonlight) enters the atmosphere, it is either absorbed, reflected, scattered, refracted,...

# Various Light Phenomena and Hertz Produced by Radio Pulses Rainbows, sunsets and halos; a spectacular display of colors and visuals in the sky called "atmospheric optics" or light phenomena. As sunlight (or moonlight) enters the atmosphere, it is either absorbed, reflected, scattered, refracted, or diffracted by atmospheric particles or air molecules. These processes, individually or in combination, are responsible for producing the most optical effects. This module investigates these particle-light interactions and the assortment of light or optical effects they produce. ## Classifications of atmospheric particles: mechanism of its occurrence, air, dust and haze; ice crystals, and lastly water droplets. 1. **Mechanisms** - Particle/Molecule-light interactions responsible for creating optical effects. This interaction includes reflection, scattering, refraction, and diffraction. 2. **Air, Dust, Haze** - Optical effects resulting from the interaction of light with air, dust, and haze particles. This effect includes crepuscular rays, blue skies, blue haze, and sunsets. 3. **Ice Crystals** - Optical effects resulting from the interaction of light with ice crystals. This effect includes sundogs, sun pillars, and halos. 4. **Water Droplets** - Optical effects resulting from the interaction of light with water droplets. This effect includes cloud iridescence, rainbows, and a silver lining along the edge of clouds. ## Mechanism 1. **Reflection of Light** - Light is said to be reflected when the angle at which light initially strikes a surface is equal to the angle at which light bounces off the same surface. Reflection can explain the origin of color in some cases because certain portions of white light are more easily absorbed or reflected than others. For example, an object that appears to have a green color does so because that object absorbs all wavelengths of white light except that of green, which is reflected. One form of reflection-internal reflection-is often involved in the explanation of optical phenomena. During internal reflection, light enters one surface of a transparent material (such as a water droplet), is reflected off the inside surface of the material, and is then reflected a second time out of the material. The color of a rainbow can partially be explained in terms of internal reflection. How about seeing your image or reflection on a concave and convex side of the spoon? * **Convex side** - this side that bulges out. A convex mirror makes what you see smaller and more so as you look closer to the edges. Convex mirrors are sometimes used to see around corners in traffic or in stores to detect shoplifters. Turn the spoon around. * **Concave side** - this side which curves inwards. If you are close to a concave mirror, you see an enlargement. A concave mirror can be useful in the bathroom when you're putting on make-up or shaving. If you back away from a concave mirror, you reach the focal point at this point, the image gets all fuzzy. If you keep moving backwards, the image in a concave mirror turns upside down. 2. **Scattering of Light** by small particles and molecules in the atmosphere. Some particles and molecules found in the atmosphere have the ability to scatter solar radiation in all directions. The particles/molecules which scatter light are called scatterers and can also include particulates made by human industry. **Types of Scattering** * **Selective scattering (or Rayleigh scattering)** - air molecules, like oxygen and nitrogen, for example, are small in size and thus more effective at scattering shorter wavelengths of light (blue and violet). The selective scattering by air molecules is responsible for producing our blue skies on a clear sunny day. * **Mie Scattering** is responsible for the white appearance of clouds. Cloud droplets with a diameter of 20 micrometers or so are large enough to scatter all visible wavelengths more or less equally. This means that almost all of the light which enters clouds will be scattered. Because all wavelengths are scattered, clouds appear to be white. When clouds become very deep, less and less of the incoming solar radiation makes it through to the bottom of the cloud, which gives these clouds a darker appearance. 3. **Refraction of Light** * As it passes from denser to less dense mediums. The bending of light as it passes from one medium to another is called refraction. The angle, wavelength, and density of that substance determine how much the light is refracted. The refraction of light by atmospheric particles can result in a number of beautiful optical effects like halos, which are produced when sunlight (or moonlight) is refracted by the pencil-shaped ice crystals of cirrostratus clouds. * As it passes from less dense to more dense mediums. When light passes from a less dense to a denser substance (for example, passing from air into water), the light is refracted or bent towards the normal. The normal is a line perpendicular (forming a 90-degree angle) to the boundary between the two substances. The bending occurs because light travels more slowly in a denser medium. **Mirages** Mirages happen as the ground is very hot and the air is cool. The hot ground warms a layer of air just above the ground. When the light moves through the cold air and into the layer of hot air, it is refracted (bent). A layer of very warm air near the ground refracts the light from the sky nearly into a U-shaped bend. 4. **Diffraction of Light** Diffraction is the slight bending of light as it passes around the edge of an object. An optical effect that results from the diffraction of light is the silver lining sometimes found around the edges of clouds or coronas surrounding the sun or moon. The illustration above shows how light (from either the sun or the moon) is bent around small droplets in the cloud. **Air, Dust, Haze** * **Crepuscular Rays** - sun rays converging on the horizon. Crepuscular rays occur when objects such as mountain peaks or clouds partially shadow the sun's rays. The name crepuscular means "relating to twilight," and these rays are observed at sunrise, and sunset. Crepuscular rays are often red or yellow in appearance because blue light from the sun is selectively scattered out by air molecules. * **Blue Skies and Blue Haze** - resulting from selective scattering by air molecules. Blue skies are produced as shorter wavelengths from incoming visible light (violet and blue) are selectively scattered by small molecules of oxygen and nitrogen -- which are smaller than the wavelength of light. The violet and blue light have been scattered over and over by the molecules throughout the atmosphere, so our eyes register it as blue light coming from all directions, giving the sky its blue appearance. * **Sunsets Appear in a Variety of Colors** - As the sun sinks toward the horizon, sunlight enters the atmosphere at a much lower angle and consequently must pass through much more atmospheres before being seen by an observer. Air molecules scatter away the shorter wavelengths of light (violet and blue). The light with longer wavelengths (yellow, orange and red) penetrates through the atmosphere produces colorful sunsets. The combination of refraction and scattering of sunlight by atmospheric particles is responsible for producing twilight, the brightness in the sky we observe even though the sun is below the horizon. As incoming sunlight passes through a denser atmosphere, shorter wavelengths of light (violet and blue) are efficiently scattered away by particles suspended in the atmosphere. This allows predominantly yellow and red wavelengths of light to reach the observer's eyes, producing a yellowish-red sunset. When there is a high concentration of particles in the atmosphere that are slightly larger than air molecules (like smoke, dust, and pollutants), shorter and intermediate wavelengths of light (violet, blue and yellow) are scattered away. Therefore, only the longer wavelengths (orange and red) reach the observer's eyes, giving the sun an orange-red appearance. Dust and ash particles injected into the atmosphere by volcanic eruptions can also cause red sunsets. **Water droplets** * **Rainbows** - is an arc of concentric colored bands that develops when sunlight interacts with rain drops. A rainbow occurs when rain is falling in one portion of the sky, and the sun is shining in another. Sunlight is refracted as it enters a raindrop, which causes the different wavelengths (colors) of visible light to separate. Longer wavelengths of light (red) are bent the least, while shorter wavelengths (violet) are bent the most. * **Primary Rainbow** The primary rainbow forms between about 40° and 42° from the antisolar point. The light path involves refraction and a single reflection inside the water droplet. If the drops are large, 1 millimeter or more in diameter, red, green, and violet are bright, but there is little blue. Such large droplets are suggested by the rainbow at right. * **Secondary rainbows** The secondary rainbow is about 10° further out from the antisolar point than the primary bow, is about twice as wide, and has its colors reversed. The light of the secondary bow is one-tenth the intensity of that of the primary bow, given the same viewing conditions. The region between the two rainbows should be a bit darker than the sky outside the secondary rainbow, but this is a smaller difference. * **Supernumerary bows** - set of interference rainbows just inside the primary rainbow. Supernumerary bows occur when raindrops responsible for the main rainbow are much uniform in size. Usually, there is some variation in size of raindrops, and the supernumeraries are washed out altogether. There is always some washing out of colors, and the bows show much green and red in them and not the other colors in the spectrum. ## Hertz Produced by Radio Pulse Recall that visible light is only one of the seven electromagnetic (EM) waves. Another type of EM wave is the radio wave which is widely used for communication and transmission of information regardless of the distance of the sender and receiver. Radio waves are naturally created by astronomical bodies or lightning. They can also be created artificially to serve their purpose. In November 1886, Heinrich Hertz became the first person to transmit and receive controlled radio waves. Considering how indispensable his wireless transmissions quickly became, it seems a little odd looking back that he had no practical purpose in mind for the radio or Hertzian waves he discovered. His research was focused solely on discovering the theory of electromagnetism was correct in 1864. According to Maxwell's theory, EM waves move at the speed of light, c = 3 x 10^8 m/s, and is created by oscillating electric and magnetic fields moving perpendicular to each other, in which a changing electric field yields changing magnetic field and vice versa. The first person to succeed was Heinrich Rudolf Hertz. In 1886, Hertz was able to create the first man-made radio wave by using induction coil, Leyden jar as a condenser and a spark gap. **Hertz' First Transmission of Radio Waves** The poles of the spark gap are made up of two 2-cm radius spheres. The picture below depicts the image of Hertz' set-up. Inducing high voltage to the induction coil caused a spark discharge between the spark gaps. Relating this to Maxwell's theory, where changing electric fields or magnetic fields will produce EM waves, Hertz thought that whenever a spark is produced, EM waves will be transmitted. To check if this was true, he created a receiver made of looped copper wire whose ends were made of small knobs with small gaps in between. He ran the experiment again and saw that a spark was produced at the receiver loop, which means that EM waves were transmitted. His experiment was the first transmission and reception of radio waves. **The Speed of Electromagnetic Waves** To calculate the speed of the EM waves, Hertz performed another experiment that aimed the radiation into a wide metal sheet. A standing wave was formed, from which he was able to measure the distance between nodes which served as the wavelength (λ) of the EM wave, while the frequency (f) was calculated from the frequency of the oscillator. From these two quantities, Hertz was able to calculate the speed of the EM wave (v=xf). The speed of the EM wave was equivalent to the speed of light, which served as a proof of Maxwell's theory. The frequency of a wave, which is the number of cycles created in a unit of time was named hertz, in honor of Heinrich Hertz. ## NEWTONIAN MECHANICS AND MAXWELL'S ELECTROGMAGNETIC THEORY Newtonian mechanics is based on application of Newton's Laws of motion which assume that the concepts of distance, time, and mass, are absolute, that is, motion is in an inertial frame. Newtonian mechanics is also known as classical mechanics, has concepts that do not entirely agree with all known theories in Physics, like Maxwell's electromagnetic theory. But when Einstein presented his theory of special relativity, the conflict between these two great ideas was resolved. Newtonian mechanics is the study of the causal relationship, in the natural world, between force, mass, and motion. Natural philosopher and 17th century scientist Isaac Newton developed a set of universal principles, elegant in their simplicity, to help explain and predict the motion of objects in the natural world, and the degree to which these objects change their relative motion by interacting with external forces. Newton embodied the interrelationship between the physical concepts of force, mass, and acceleration into his three laws of motion. The ability of these mechanics to accurately describe natural phenomenon under observation is derived from the application of these distinct laws of motion. **"A frame of reference which is at rest or moving with constant velocity is known as inertial frame of reference"** 1. The first law of motion holds that a body in motion tends to remain in motion, and a body at rest tends to stay at rest. This principle explains the concept of inertia, namely, the application of force that is required to move a stationary object. Similarly, the deceleration of a body, otherwise moving at a constant speed, can only occur when an outside force acts on it. For example, a bullet fired from a rifle would continue its motion in a certain direction perpetually, were it not for the simultaneous forces of gravity and the resistance of the air in the atmosphere. These forces act together on the bullet to cause it to stop at a certain distance. * **Static friction** is the type of friction that exists between a stationary object and the surface it is placed on. It prevents things from moving around when we place them somewhere. The glass that is probably on your table right now is standing still because of static friction. Even if things are slightly tilted, static friction can work its magic to and extent. * **Sliding friction** is the type of friction that occurs between two objects that are sliding against each other. In sliding friction, there is always another force involved. This force makes the object move. By pushing an object, we create sliding friction; it is as simple as that. * **Rolling friction**, also known as rolling resistance, is the force that slows down rolling balls or wheels. It slows down their motion, to be exact. Interestingly, rolling friction is also the reason why things start to move in a rolling motion in the first place. If we apply some sort of force to a wheel that is not moving, small static friction is holding it back from starting its rolling motion. 2. Newton's second law of motion is a mathematical or quantitative formula that describes the inherent nature of force. Newton postulated that the amount of force exerted is directly proportional to the mass of a body, times its acceleration, or f=ma. If two distinct bodies are moving at a constant acceleration, the object with the larger mass will produce the greater force. This principle can be illustrated by the example of an automobile and a locomotive that are traveling towards each other at an equal rate of speed. When the two objects collide, the force exerted on the automobile will be vastly greater due to the much greater mass of the locomotive. 3. The third law of motion can be summarized with the statement for every action, there is an equal and opposite reaction. In other words, the forces of two bodies acting upon each other are always equal and directly opposite. For instance, the force that a baseball exerts on a bat is equal and opposite to the force that the bat exerts on the baseball. How did theory of special relativity resolve this conflict? Newtonian or classical mechanics discusses the everyday motion of the objects of normal size around us, including the force that causes these motions. The concepts under Newtonian mechanics are mainly based on ideas of Newton about motion. It describes the state of motion of an object, whether at rest or moving in a straight path, with the forces that maintain it, and can cause changes in the body's states of motion. Maxwell's electromagnetic theory consists of four formulas gathered from the different works of Faraday and other physicists that unites all the concepts of electricity and magnetism and findings that electric and magnetic fields spread as waves. In 1886, Hertz proved that these waves really exist and the propagation speed of these waves can be calculated using the formula: c = 1/sqrt(εoμo) where: * c = the speed of light * εo = the electric field constant * μo = the magnetic field constant Maxwell observed that the value of the above expression is equivalent to the speed of light c (3.0 x 10^8 m/s), which implies that speed of light c must also be constant. This is where the conflict between Newtonian mechanics and Maxwell's theory starts. If we consider a moving object of speed 100 m/s and placed a switched-on flashlight in it, according to Newtonian mechanics, the speed of the light coming from the flashlight in this scenario would be 100 m/s + c, and this contradicts what Maxwell's theory tells that speed of light is a constant value. The theory of special relativity proposed by Einstein in 1905 explains the problems that involve motion of frames of reference at constant linear velocity with respect to one another and describes the motion of particles in an inertial frame of reference with speeds ranging from zero to a value close to the speed of light in vacuum. This theory is based on two postulates: 1. The laws of Physics are the same in all inertial frames of reference moving with constant velocity relative to one another (principle of relativity) 2. The speed of light is the same in all inertial frames of reference (constancy of the speed of light). The second postulate clearly tells that Maxwell's idea is correct but does it mean Newtonian mechanics is wrong? Not totally, but the postulates of Einstein tell us that Newtonian mechanics has limitations in terms of its application. If we consider moving objects with very slow speed compared to the speed of light, Newtonian mechanics applies like the speeds of a flying ball and running car. But if we consider speeds that are closer to the speed of light, a new concept must be included to supply the limit of Newtonian mechanics, and that is the Lorentz transformation, which is the counterpart of the Galilean transformation of the Newtonian mechanics. ## The Special Relativity Theory Special relativity is an explanation of how speed affects mass, time and space. The theory includes a way for the speed of light to define the relationship between energy and matter small amounts of mass (m) can be interchangeable with enormous amounts of energy (E), as defined by the classic equation E = mc^2. Special Relativity Theory is a theory that predicts events measured with various observers who are in motion in respect to the event. An "event" is just a physical happening, e.g., exploding firecrackers, a passing rocket, or a flash of light. What's so "special" about the Special Relativity Theory? It is because each observer's reference frame or perspective is a special type of reference frame called inertial reference frame. This means that the observer is at rest and not accelerating from the observers' perspective. For example: * Observer A is sitting at a train station. Observer A's position is an inertial reference frame because he/she is at rest or does not move from his/her perspective. * Observer B is sitting on a train approaching the train station with constant velocity. Observer B's position is still an inertial reference frame because although the train is moving, it is not accelerating, or not gaining or losing speed. But are they not truly moving? In this case, the answer is yes, because, in Special Relativity Theory, the effect of gravity, the Earth's rotation, and its revolution around the sun are neglected. **The Special Relativity Theory has two postulates or assumptions:** 1. The Relativity Postulate, where it is assumed that the laws of physics are the same in all inertial reference. 2. The Speed of Light Postulate, where it is assumed that the speed of light in vacuum is always the same. **Consequences of the Postulates of Special Relativity Theory** 1. **Relativity of Simultaneity** The relativity of simultaneity is the concept that simultaneity-whether two events occur at the same time-is not absolute but depends on the observer's frame of reference. According to the theory of special relativity, it is impossible to say in an absolute sense whether two distinct events occur at the same time if those events are separated in space, such as a car crash in London and another in New York. The question of whether the events are simultaneous is relative: in some reference frames, the two accidents may happen at the same time in other frames (in a different state of motion relative to the events), the crash in London may occur first, and still in other frames, the New York crash may occur first. If the two events are causally connected (“event A causes event B"), then the relativity of simultaneity preserves the causal order (i.e., “event A causes event B" in all frames of reference). Imagine one reference frame assigns precisely at the same time to two events that are at different points in space, and a reference frame that is moving relative to the first will generally assign different times to the two events. This is illustrated in the ladder paradox, a thought experiment which uses the example of a ladder moving at high speed through a garage. 2. **Time Dilation** One of the effects of special relativity is time dilation, which is the difference of time interval between two events measured by an observer in a stationary frame and by another observer in a moving frame. The dilated time interval is longer than the proper time interval and is given the symbol t'. The equation for time dilation is given by: t' = t/sqrt(1 - v^2/c^2) where: * t' = time measured from an observer outside the frame of reference. * t = time measured from an observer inside the frame of reference. * v = speed of the object * c = speed of light The famous example of time dilation is the twin paradox as seen in the sample problem. **Sample Problem:** John left for a round trip to a distant star in a spaceship at a speed of 0.95 c relative to Earth. According to those operating the control station on Earth, the trip took 15 years. How long was the round-trip according to a clock on board the spaceship? Suppose John had a twin brother Jose. How old would they be upon John's return if John was 32 years old when he left for a trip? Given: * v = 0.95 c * t' = 15 years Solution: The event in this example is the round-trip to a distant star. Rearranging the equation and substituting the given values to solve for proper time interval, John's age = 32 + 4.7 = 36.7 years old Jose's age = 32 + 15 = 47 years old 3. **Length Contraction** Another consequence of special relativity is that an object moves at speed near the speed of light experiences length contraction as measured or seen by someone in a reference frame that is moving with the object. The contracted length is given by: L = L0 * sqrt(1 - v^2/c^2) where: * L = contracted length * L0 = proper length (i.e., the length measured by the observer at rest with the object) * v = the speed of the moving frame relative to a fixed frame * c = the speed of light **Sample Problem:** A spaceship traveling at 0.5c relative to Earth is 45 m long and 62 m wide as measured by its crew. What are the dimensions of the spaceship as measured by the mission control on Earth? The spaceship is traveling parallel to its length. Given: The proper dimensions of the spaceship are those determined by the crew. * L0 = 45 m * W0 = 62 m * v = 0.5c Solution: There is no contraction as far as the width is concerned because it is not along the direction of motion. Therefore, the width of the spaceship as measured by the mission control on Earth (W) is also 62 m. There will only be contraction along its length. Solving for L, L = 45 * sqrt(1 - (0.5)^2) = 39 m 4. **Mass - Energy Equivalence** A major consequence of special relativity is the mass-energy equivalence given by the famous equation: E = mc^2 This means that mass and energy are equivalent. A gain (or loss) in mass maybe considered a loss (or gain) in energy. This is true for nuclear reactions, which may be classified into nuclear fusion and nuclear fission. Nuclear fusion is a process in which a nucleus combines with another nucleus. On the other hand, nuclear fission happens when a large nucleus breaks into smaller nuclei, accompanied by the emission of neutrons and a large amount of energy. An example of a fission reaction is the decay of Uranium - 235. Uranium - 235 interacts with neutrons, an unstable Uranium - 235 is formed, which immediately disintegrates into Barium and Krypton. 5. **Cosmic Speed Limit** The speed of light is widely known to be the absolute pinnacle of movement. When Albert Einstein first entwined mass and energy in his Theory of Relativity, it established the Universe's speed limit at 299,792 kilometers per second (186,282 miles per second). According to Einstein, nothing in the Universe that has mass could either match or move faster than light. But that doesn't mean that nothing can move faster than light. In truth, physicists have discovered several phenomena that can match and beat (in specific respects) the speed of light. And several theoretical models posit specific ways that the speed of light could be surpassed.