Electromagnetic Radiation PDF

Electromagnetic Radiation Let’s make waves EMR Electromagnetic Radiation is a radiant energy form, that travels outward from a source location Common Forms: - Radio - Heat - Light - Heat - X Rays - Gamma rays - UV rays EMR is classiﬁed by its frequency and its wavelength. EMR Waves: “disturbance that moves outward from its point of origin, Identiﬁcation transferring energy through a medium by means of vibrations.” EMR is discussed as a wave and as a particle. As we progress through this unit we will discuss the validity of each model, as both have strong evidence to support them. EMR When discussing EMR as a wave we will use the universal wave equation. Calculations v=fλ Where v is velocity, f is frequency, and lambda is the wavelength of the light. Wavelengths describe the length between a given crest of a wave and the next crest. It can also be measured from trough to trough if you prefer. Waves Get on my wavelength. In the discussion of EMR as a wave, it is important to remember that wavelengths vary from several Waves kilometers to femtometers (10-15) Each given wavelength corresponds to Wavelengths a diﬀerent area of the electromagnetic spectrum The electromagnetic spectrum NOT TO SCALE - NOT TO SCALE - NOT TO SCALE - NOT TO SCALE - NOT TO SCALE - Electromagnetic Spectrum Prior to probing deeper into this discussion please mark oﬀ page 638 in your textbook. Wavelength and frequency charts are not provided for all examination questions; it is expected that the general regions of each radiation form are memorized. Frequency describes the amount of times a wave will cycle from crest to a new crest in a given time period. We use the following equation to On Frequency relate frequency and time T = 1/f It's all Vibrations man T is the period in seconds, and f is frequency in s-1 more often referred to as Hz (Hertz) or cycles per second. Given the universal wave equation v=fλ We can determine that wavelength Relationships and frequency are linked values. Assuming the value for velocity Wavelength and frequency have remains the same, what must happen an important one. to the wavelength if the frequency is doubled? The relationship between frequency and wavelength is considered inverse Inverse or a 1/x relationship. When one value increases the other Opposite must decrease proportionally. When discussing EMR in a vacuum it is assumed that all EMR travels at the speed of light. 3.0x108 m/s Cosmic Speed Limit We can use this to derive the Don't get a cosmic Ticket following equation c =fλ Where c is the speed of light. Practice Questions A sample of EMR is travelling in the At a local lab in Edmonton Alberta deep vacuum of space. It is determined a sodium sample is heated until it that the frequency is 600 cycles per begins to glow red; the wavelength second. of the emitted EMR is 700 nm what is its frequency? What is the wavelength of this EMR sample What is its period? Energy in relation to EMR at this time can be tied to the frequency of a wave. A high frequency wave must have a Energy very short wavelength, and has a high energy level. The higher the energy level the more damage a wave can do. Think of a tsunami vs a wave pool. --Energy can be an issue-- The next 8 slides will discuss our primary categories of EMR, from lowest energy to highest. Each slide contains Upcoming Slides Frequency Wavelength Info straight from the textbook Energy Production method And any important facts. EMR from the textbook - Radio/Radar Radio utilizes a long wavelength with a relatively low frequency. This means it is reasonably low energy. It is produced by oscillations of electricity in an antenna f = 104 - 1010 Hz λ = 104 - 10-2 m Radio is safe and highly utilized, however it requires strict government control due to its ease of use and safe propagation. It can easily be interfered with. Microwaves Microwaves are commonly used for heating food via a natural resonance with water. Its shorter wavelength makes it less likely to be interferred with in communications Still a lower energy wave Produced by oscillations within special tubes or Solid state devices f = 109 - 1012 Hz λ = 10-1 - 10-4 m Has been linked to some forms of cancer, can damage living tissues Infrared (larger than red) Infrared is generally felt as heat. It can be used by remote sensing devices such as IR cameras or spectroscopy Created via the motion of particles, or the transition of electrons through valence shells Low energy f = 1011 - 4.0 x 1014 Hz λ = 10-3 - 7.5 x 10 -7 m Can burn skin with over exposure Visible light spectrum Visible light is the area of the spectrum our eyes perceive. Everything we “see” is visible light. This EMR is created from the higher level energy transitions involving valence electrons. This is a medium energy spectrum. f = 4.0 x1014 - 7.5 x1014 Hz (narrow band) λ = 7.5x10-7 - 4.0x10-7 m (narrow band from red to violet) Some limitations to the visible light spectrum relate to small objects, when particles become small enough they are eﬀectively masked altogether and invisible within this narrowband. This is a force known as diﬀraction. Ultraviolet Ultraviolet is the light just after the visible spectrums violet band. It can be easily absorbed by objects, causes ﬂuorescence, tans, and kills bacteria. A high energy emission, caused by even higher level energy transitions in valence electrons f = 7.5x1014 - 1017 Hz λ = 4.0 x 10-7 - 10-9 m Big cons to this spectrum is the danger to human tissue. Ultraviolet light is carcinogenic and a known mutagen X Rays This very high energy emission can penetrate most matter, and is absorbed by denser material like bones. Can destroy mutagenic, or cancerous cells if targeted correctly This form of radiation is produced by electron shifts in an atom or the sudden acceleration of free electrons. f = 1017 - 1020 Hz λ = 10-9 - 10-12 m Prolonged exposure is cancerous and can cause mutations Gamma Rays Gamma rays are Extremely high energy radiation, that can penetrate most matter and destroy cancerous cells on a local level. Can be used to probe structures as it moves unimpeded through most matter. Created by the decomposition of unstable nuclei, or the sudden negative acceleration from a high energy particle accelerator. f = 1019 - 1024 λ = 10-11 - 10-16 m Highly dangerous, can cause radiation sickness and death. Cosmic Radiation Penetrates matter very deeply; largely used for study about the universe’s origins Extremely high energy wave, created by the continuous bombardment of the earth's atmosphere by high energy particles from space. f = 1024 Hz or greater λ = 10-16 m or smaller Extraordinarily lethal. Can cause radiation sickness and death. Competing models EMR as mentioned earlier has been described as a particle and as a wave. We will ﬁrst be discussing the wave model of light, and the supporting evidence of this model. It is important to note that neither waves nor particles is a wholesale correct answer for what EMR is. History of the Wave Model The wave model was ﬁrst proposed by Dutch Mathematician Christian Huygens. It was proposed that light waves could in fact interfere with each other, develop interference patterns and wave fronts, travelling in straight lines from a common origin point. The primary diﬀerence of EMR waves from traditional mechanical waves is: EMR does not require a medium to travel through. This idea was largely ignored at the time, as Newton’s theories of the particle model were far more popular. However Thomas Young’s double slit experiment proved the core tenets of the wave model Double slit - Take 1 We will be revisiting this experiment several times to peel back the layers. At ﬁrst glance however we can see that the experiment does show interference patterns in the light, lending support to a wave model Maxwell's Electromagnetic Theory James Clerk Maxwell is a scottish mathematical physicist who combined mathematical calculations with experimental evidence to create a framework for understanding EMR. Maxwell proposed that a changing electric ﬁeld, would generate a proportional changing magnetic ﬁeld; and the interaction of these two ﬁelds would propagate through 3D spacetime as a wave In his theories he linked the ideas of electricity and magnetism generating our current understanding of “electromagnetism” Electric & Magnetic Fields Reloaded Faraday’s understanding of electric ﬁelds in a conductor lead to the understanding that charged particles can generate a magnetic ﬁeld that is Perpendicular to the Current Maxwell regularly did work with capacitors. He found that the electric ﬁeld surrounding a capacitor, could generate the same eﬀect as a current through a conductor. In shorthand, a changing electric ﬁeld, can create a changing magnetic ﬁeld. Maxwell Equations Maxwell concluded that a conductor was not necessary for a electromagnetic wave to exist. Using Calculus Maxwell created mathematical equations that described his theory; these are rather famous and will be studied in any university. They are called the maxwell equations Unfortunately calculus is beyond our scope, so you will have to take my word for it. 3D model of Electromagnetic Wave The strength of the electric wave at any given moment will be proportional to the magnetic ﬁeld at any give moment. It is important to know that the electric ﬁeld will always be 90 degrees to the magnetic ﬁeld. Maxwell's Predictions The maxwell equations not only correctly predicted the existence of electromagnetic waves it also allowed for predictions of the wave properties 1. Electromagnetic waves are produced whenever an electric charge is accelerating. Therefore as an electric charge oscillates, electrical energy will be lost, and equivalent amount of energy will be radiated outward in the form of oscillating electrical and magnetic ﬁelds Maxwell Predictions 2. When the electric charge is accelerated in periodic motion, the frequency of the oscillation of the charge will correspond exactly to the frequency of the EM wave 3. All electromagnetic waves will travel at a speed of 310740000m/s and obey the universal wave equation. Relating speed, frequency and wavelength. (look how close he got to predicting the speed of light!) 4. The oscillating electric and magnetic ﬁelds will always be perpendicular to each other and perpendicular to the direction of propagation of the wave. Maxwell Prediction 5. Electromagnetic waves should show all the phenomena associated with transverse waves. Interference, diﬀraction, refraction, and polarization. The last prediction directly correlates to the wave model of EMR and relates predictions to experimental evidence. German physicist that designed an experiment to detect and produce EMR. Heinrich Hertz It consisted of a set of capacity spheres connected to high voltage “Hertz Donut” current. He also set up an antenna loop to detect the potential EMR emission Hertz Experiment Relating Theory and Practice Maxwell uses the term changing frequently in his original proposal. His understanding was that a “changing” electric ﬁeld was critical to creating an electromagnetic wave. This is where an induction coil was important to Hertz original design. The induction coil rapidly changed the electric ﬁeld across the spark gap. When this ﬁeld jumped from one electrode to another. As the charge was rapidly transferred the electric ﬁeld underwent a rapid change that caused a changing magnetic ﬁeld, which caused a changing electric ﬁeld and so on. An EM wave was rapidly produced in all directions. Extensions Hertz was able to detect the EMR because the radiation induced a predicted current in the antenna loop. Subsequent experiments allowed him to produce a standing wave and measure the wavelength and frequency of the EMR. He was able to verify that the waves did follow the Universal wave equation. Two years later engineers started using EMR to produce radio waves, and ny 1901 radio waves were being transmitted across the atlantic ocean. This is one of the single most inﬂuential breakthroughs in the 19th century. Practice Read Chapter 12.1 in Textbook Complete Questions on page 647. Workbook pg. 188 -193 SNAP book: read pg. 143. The speed of EMR The ﬁrst recorded attempts at recording the speed of light were largely failures. Empirical As the story goes Galileo stood atop a Determination hillside about a kilometer from his assistant on an opposing hill. Using a series of lanterns and his pulse rate he Story Time attempted to measure the speed of light. It was a failure, light can travel 2km in 0.000 006 667 seconds. Critical Thinking: Measuring the Take 5 minutes to think to yourself speed of light. how you might go about measuring the speed of light. There are a large number of novel ways to try it. Second attempt. If posed with the problem how would YOU approach it. Olaus Romer and Huygens attempted to solve the problem using one of Jupiter's easily visible moons (IO) Measuring the Knowing when the eclipse should Speed of light take place it was easily monitorable. However the eclipse happened later than expected. This was due to the earth's orbital rotation increasing the distance, and thus forcing the light to take longer. Mathematics behind light With some estimations the earth's orbital diameter was approximated to be 3.0x1011m. The discrepancy between the expected eclipse and the sighting of the event was about 22 minutes. With these known values, can you calculate the speed of light as it is experimentally achieved in this context. It's worth noting that their value was What is the % error or % diﬀerence of considered impossibly large and was not even the experimental value close to acceptance until long after their deaths. Accuracy When we compare results the accuracy of your result matters. When discussing accuracy we use the following formula, this is not on your formula sheet but it is very intuitive. This ﬁnds the percent diﬀerence. Accepted value - measured value ------------------------------------------- x 100% Accepted value Continued attempts at ﬁnding the speed of light. In 1848, armand Fizeau became the ﬁrst person to successfully measure the speed of light on the surface of the planet. His apparatus featured a a rotating toothed gear, a light source, some lenses, and a mirror. In his experiment, light was allowed to pass through one of the gaps on the gear, travel a known distance and then reﬂect back through the next gap in the gear. The gear would slowly be adjusted in speed until the light would be observed in the next gear tooth. Accuracy Fizeau measured the speed of light within 5% percent change of the now currently accepted value. What was the speed he found? How accurate was his value? What is the percent diﬀerence Does the medium matter? Fizeau was not ﬁnished toying with light. His next experiments featured shining light through a series of tubes ﬁlled with water. Light from a single source emitted travels the same distance through two water tubes travelling in diﬀerent directions. If the light’s patterns show interference it would prove that the medium would have a role to play in the speed of light. Medium matters Its worth noting that when discussing the speed of light in this experiment both the medium and direction of the water ﬂow played a role in changing the speed of light. This experiment concluded that the medium EMR travels through directly inﬂuences the speed that EMR will travel at. Michelson’s experiment Albert Michelson took his attempt at solving the speed of light in 1905. Building upon the experimental design of Fizeau he decided to shine light a known distance, and use a turning mechanism to mark the exact passage of time. Whereas Fizeau used a toothed wheel, Michelson used an octagonal mirror. He reﬂected the light oﬀ of one of the mirrors, that then reﬂected the light on a 35 km course. The octagonal mirror would turn in the meantime. If the frequency of the mirrors lined up correctly the light would be reﬂected back to the observer. Michelson Michelson calculated that at precisely 32,000 rotations per minute he could observe the light. 1. What is RPM in Hz 2. Using our knowledge of frequency and period calculate his experimental speed of light. 3. What was his percent diﬀerence from accepted value, and the percent change? Practice Textbook Pg. 650 and 652 Workbook Pg 194 - 202 SNAP pg 224 Reﬂection Refresher The speed of light was measured to be 2.97x108m/s using a 16 sided set of rotating mirrors and a ﬁxed mirror separated by 5.00x103m. At what frequency was the mirror rotating? Ensure you have tried the application and extension questions from the textbook pg. 652. Intro to Reﬂection Consider what we already know: - Reﬂections allow us to see objects separate from their position. Consider a mirror or a still lake as an example of this. - What happens to the mirror if it is scratched, or the lake if a strong gust of wind kicks up? Vocabulary Light travels in straight lines in a consistent, uniform medium. This is called Rectilinear propagation When light falls on a smooth ﬂat surface it undergoes specular or regular reﬂection. In the case of a fresh mirror or a still lake many of the incident or incoming rays of light can reﬂect in even parallel reﬂected rays. In the case of the scratched mirror or the disturbed lake the light undergoes diﬀuse or irregular reﬂection. Specular vs Diffuse Reﬂection As seen on the right we can observe the path of the light rays. When the light encounters a rough surface it becomes disorganized and prevents coherent images from forming. The images to the right are known as a ray diagram The law of reﬂection. Reﬂection will occur if an incident light ray, contacts a polished, reﬂecting surface. The ray makes contact at a position known as the point of incidence and then leaves the reﬂecting surface. After leaving the surface the ray is now called a reﬂected ray. At any point of incidence an imaginary line called the normal line (N) is drawn perpendicular to the surface, the angle of incidence is the same as the angle of reﬂection. Summation of the Law The Angle of reﬂection is equal to the angle of incidence and is in the same plane. If the given angle of incidence was 25 degrees relative to the normal line, then the resulting angle of reﬂection is 25 degrees relative to the Normal line. Image Formation When light is reﬂected oﬀ of a reﬂecting object such as a mirror the image formed is not the actual object. Consider writing a note to yourself and then trying to read it through a mirror. The image presented is not identical to the object in reality. In the above ﬁgure notice how For this reason we refer to images that what the eye perceives is a distant image in a straight line are viewed from a reﬂective surface to be with the label opposite to how “virtual objects” it is in reality. Real vs Virtual images Virtual Image: The term ascribed to images seen in reﬂecting objects. Real image: A real image is only formed on a diﬀuse or non reﬂecting object. An image drawn on a non reﬂecting object like paper, is a real image. An image viewed through a mirror is a virtual image. Characteristics of Virtual Images. We describe virtual images with four characteristics: - Magniﬁcation - Attitude - Position - Type Magniﬁcation refers to the objective size of the image. The magnitude can be enlarged, reduced or unchanged Attitude and Position The attitude of a virtual image refers the orientation of an image. Attitude is either erect or inverted. The image to the right shows a trees image that has been vertically inverted. Images can be horizontally inverted, such as the writing on a page. Position refers to where the image appears relative to the Surface of the mirror or reﬂective object. Image Type As discussed earlier images in regards to a reﬂecting images surface are either real or virtual. The textbook contains a handy “razor” to determine if an image is real or virtual. Real Images: Can be projected onto a screen or another object. Virtual Images: Can only be seen or photographed, they can not be projected. Why is this important? Consider an ambulance sign, if the use case of a virtual image was not considered the word ambulance would be illegible in a rearview mirror Curved Mirrors There are many types of curved mirrors that will be discussed, however the ﬁrst is a spherical mirror, of which we can discuss both convex and concave applications of. Convex spherical mirrors are used as a common anti theft device due to their unique properties. To the right we can see how the term spherical mirror is derived. We ﬁrst consider an entire polished sphere inside and out, then choose a segment to use. Curved Mirrors By removing a segment of the sphere we produce a double sided spherical mirror with a concave side and convex side. The convex side is referred to as a diverging mirror as its surface causes parallel light to spread or “ diverge” after being reﬂected. Concave mirrors. Concave Mirrors are referred to as convergent mirrors. Parallel light rays converge together after being reﬂected from this surface. As with plane mirrors a ray diagram can be helpful to illuminate how images will be formed in certain contexts. Given that these are more complex Situations the terminology will also expand in complexity. Vocab Center of curvature (C) : The point in space that would represent the center of the sphere from which our curved mirror is cut. Radius of curvature (r) : the distance from the center of the curvature to the mirror surface. Vertex (V) : The geometric center of the curved mirror surface Principal Axis (PA) : An imaginary line drawn through the vertex, perpendicular to the surface of the curved mirror. To be continued on next slide. Vocab continued Principal Focal Point (F) : The point where light rays that are parallel to and close the principal axis converge, or appear to diverge from, after being reﬂected. Focal Length (f): The distance from the vertex to the focal point, measured along the principal axis. The focal length is related to the radius of the curvature by f=r/2. This means that as the radius of curvature is reduced, so to is the focal length of the reﬂecting surface. Applied Vocab Drawing Rays on Curved Mirrors The 4 general image characteristics discussed for plane mirrors apply to curved mirrors as well. (Magniﬁcation, attitude, position, and type) To link the idea of a plane mirror to a curved mirror we will consider the Normal line discussed earlier as an extension of the radius drawn at that point. The law of reﬂection will still describe the way that incident rays will be reﬂected. (Application practice coming soon) Drawing Rays on Curved Mirrors To predict how an image will appear on a curved mirror we will need to draw three distinct rays, the law of reﬂection,the mirrors focal point, center of curvature, and vertex. LOTS of information. Lets ﬁrst discuss the three rays being drawn. - 2 of the rays will determine the corresponding location of the image in the reﬂection - The third ray will verify the location of the image. Ray 1 Incident Ray 1 travels in a line parallel to the principal axis from a point on the object to the mirror. Any ray that is parallel to the PA will reﬂect through the focal point on a convergent mirror, or appear to have originated from the focal point on a diverging mirror. Ray 2 Incident Ray 2 travels from a point on the object toward the focal point. Any ray that travels through the focal point on a converging mirror, or is directed at the focal point on a diverging mirror, will be reﬂected back parallel to the principal axis. Ray 3 Incident Ray 3 travels from a point on the object toward the center of curvature Any ray that passes through the center of curvature on a converging mirror, or is directed at the center of curvature on a diverging mirror will be reﬂected directly back along the incident path. A few conventions - Objects are often drawn as erect arrows for simplicity sake, be careful how you choose to draw objects complexity begets complexity. - Real Rays are solid Lines - Virtual rays (rays created behind a mirror to illustrate a point) are drawn with dashed lines. - Lets now draw a few examples in another screen - For future reading the examples are pulled from pg. 658 of the textbook. Real vs Virtual with curved mirrors The concave image to the right will develop an image that is diminished, inverted, and maybe most importantly real. Why is it real? Consider using our razor from earlier, if a sheet of paper was placed at point I the image would be projected onto the page. Images that can be projected are considered real images. Real vs virtual with curved mirrors. In a divergent mirror as seen to the right, the image appears to be coming from behind the mirror. If you were to place a sheet of paper at the space where the image appears to be the incident rays would never reach it. You can photograph a convex mirror and whatever is on the mirror will remain, but there is no place you could place a screen to capture the reﬂection as you observe it. Characteristic of Images in Curved Mirrors Consider looking at yourself in a well polished spoon. The distance of the object to the vertex of the mirror has an eﬀect on the observed image. When the object is distant, and outside of both C and F the apparent image will be inverted and diminished, and also real When the object is close, inside of the region F, the image will be erect, enlarged and virtual. It will also become very hard to distinguish https://www.physicsclassroom.com/Physics-Interactives/Reﬂection-and-Mirrors/Optics- Bench/Optics-Bench-Interactive Image Characteristics of Converging Mirrors Object Position Characteristics Distant Real, inverted, and diminished close to F Outside of Curvature Real, inverted, and diminished between F and C At the center of Real inverted, and same size at C Curvature Between the focal point Real, inverted, and enlarged beyond C and center of Curvature At Focal Point F Undefined (no image) at infinity Between the Focal point Virtual, erect, and enlarged, behind mirror and vertex Homework Textbook: Read pg 653 - 660 (plus prior sections of Ch.13 if not yet done) Textbook: Questions on pg. 647 and 652 Workbook. Pg 185 - 202 SNAP: Read Pages 141 - 152 SNAP: Complete practice on pg 153 - 156 (some may not be doable today) Reﬂection but with Math this time. Quick Refresher An object is held behind C above the principal axis An object is held directly above the focal point of a in front a of a concave mirror. concave mirror. Describe the expected image, if there is one. Describe the expected image, if there is one, in terms of magniﬁcation, type, attitude and position. Today’s lesson will be truncated to allow meaningful practice of the concepts. Reﬂection Refresher (concave) 1. Any Ray that is travelling parallel to the PA - Images are inverted when at the focal point will reﬂect through the Focal Point of the ray or behind diagram. - Images are diminished when behind the 2. Any Ray that travels through the focal point center and magniﬁed when closer to the lens on approach to the mirror will reﬂect parallel - Images are non deﬁned when the object is at to the PA the focal point 3. A ray travelling through the center point of - Images are identical in magnitude at the the sphere will be reﬂected directly back in center. the direction it came from. - Images are in front of the object up to the center, then change to behind. - Images become virtual after the focal point - (this is a lot to remember but the math will help shorten it up) A few relationships C is twice the size of the focal point, which is to say that the focal point is ½ C The focal length is also ½ of the radius. Meaning from smallest to largest we have the focal length, then the radius which is 2f, which is the same as the radius which is C. Understanding and Calculations The expected image will be found at the convergence point of the rays. Given the two rays on the right; where is the expected image going to appear? The Mirror Equation (easy, then hard, then easy) The Mirror Equation(s) are the formulae shown to the right of this text box. The variables represent the following. f = focal length do = is the object distance di = is the image distance ho = is the object height hi = is the image height Practice Problem An object is located 20.0 cm from a converging mirror that has a focal length of 15.0cm. A. Where will the image form relative to the mirror vertex B. If the object has 5.00cm high, determine the attitude, height, and magniﬁcation of the image. Practice Problem A concave Mirror has a focal length of 10cm. An object is 18cm away from the mirror and the object is 9.0cm tall. Determine the image height and the image distance. Try this one totally solo, it's a good habit to try and apply partial knowledge to a new situation and see where you get stuck. Sign Conventions The sign conventions for the given quantities in the mirror equation and magnification equations are as follows: f is + if the mirror is a concave mirror f is - if the mirror is a convex mirror di is + if the image is a real image and located on the object's side of the mirror. di is - if the image is a virtual image and located behind the mirror. hi is + if the image is an upright image (and therefore, also virtual) hi is - if the image an inverted image (and therefore, also real) Deriving the equations Deriving the mirror equations are a bit sticky. While it is important to know how to use the equations it can be equally important to grasp how we arrive at them. Ensure you read pages 661 - 662 to help bolster your understanding of the following discussion As a class we will be covering the derivation of these in greater detail in future lessons. Refraction Refraction Consider: Placing a pencil into a glass of water, or a paddle into the lake. Often the object will appear as though it has bent in the new medium. This is refraction Other common examples of refraction include: - Rainbows - Mirages over hot land masses What is Refraction Refraction is a change in lights direction due to a change in its speed. As we know from previous experimental evidence the speed of light will be changed based on the medium it is travelling through. Therefore: Light speed changes as it travels from one medium to the next. Refraction appears when the speed of light happens on an angle Refraction Refraction occurs when light enters a new medium at an angle. Not all of the light is Refracted, some of the rays are partially reﬂected, and some are partially refracted when it transitions from one medium to the next. The process is described by an incident ray, a reﬂected ray, and a refracted ray. Connections As we know from previous lessons, the angle of incidence is equal to the angle of reﬂection and is measured about the Normal Line The Angle of Refraction is also measured against the Normal line. When the light is refracted to a slower medium it bends towards the Normal Line. When it moves from a slower medium to a faster medium it bends away from the Normal Line Refractive Index Medium Index of Refraction Vacuum 1.0000 The amount the light will Air 1.0003 bend is based upon its refractive index. The lower Water 1.33 the refractive index the faster Quartz Glass 1.47 the light will bend, the higher Zircon 1.92 the index the slower it will Diamond 2.42 travel. Due to the similarity of These values are experimental values for yellow Sodium light. A more complete index is in your vacuum to air, we often textbook Pg. 667. This table will NOT need to be consider them to be memorized. eﬀectively the same. Applying Refraction To calculate the values in the prior table we can simply take the ratio of the speed of light in a vacuum and compare it to the measured speed of light in the given medium. The formula is: n = c/v Where n is the refraction index value. Quick Problem: If Lucite has a refractive index of 1.52, what is the measured speed of light in this substance What are the units for a refractive index value? IMPORTANT Neither the basic refraction index formula, nor a refraction index table is on your formula sheet. You will be expected to memorize how to obtain experimental refractive index values from a question or utilize other formulas to obtain the value. Snell’s Law of Refraction The phenomena of refraction was observed for a very long time prior to anyone identifying the relationship that takes place. Dutch mathematician Willebrord Snell (1580-1626) identiﬁed the relationship that takes place when light changes mediums. Snell's law states Where the constant is n for a given material Limitations This version of Snell’s law works excellent for any transition from air to another medium. If you recall the constant for air is 1, and thus we only concern ourselves with n value of the second medium If the ﬁrst medium is not air or a vacuum then we must elaborate on the law to account for two unique n values. Snell’s Law reloaded In this new form of Snell’s law the angle of incidence is changes to theta 1, angle of refraction becomes theta 2. The two angles are now related to two constants. n1 is the refractive index value for ﬁrst medium, and the n2 is the refractive index for the second medium. To the right is a common rearrangement of the law. Application of Snell’s Yellow light travels from water into crown glass. The light rays are incident to the crown glass at an angle of 35 degrees. Calculate the angle of refraction. The refraction index from the textbook is 1.52, and the value for water is 1.33. Back to Waves Can we related the understanding of light refraction to our understanding of waves. Recall that we can calculate the speed of a wave given the universal wave equation. v=fλ Experimental evidence has shown that light transmitting through a medium has no direct impact to the frequency of the light; though, the velocity is changing. What can be concluded? Why isn't the frequency changing? If the frequency changed at the point where light transitions between mediums there would be what is called a pile up. Where the light would be slowed down. Think about the transition point like a 3 lane highway converging to a single lane road. Or a single lane road turning into a three lane highway. In both cases there is a noticeable change in the density of cars. This if we were to consider it as though it were light would create a noticeable pileup of waves at entrance and exit points of mediums. For this reason and several other experimental pieces of evidence we determine wavelength will change, not frequency Snell’s Law expansion To accomodate for our understanding that the refraction of a ray of light through a given medium is related to the wavelength we can further expand Snell's Law. We can now compare diﬀerences of wavelength to the changing angle through mediums Furthermore. Because Frequency is not changing between mediums we can infer that velocity changes proportionally to the wavelength exclusively. We can again further expand Snell’s Law with this understanding. Transitive Property In Math 20-1 and 20-2 you are introduced to the transitive property. The transitive property states that if a=b and a=c, then b=c. Eﬀectively if multiple things are equal to each other we can relate them together using deductive reasoning. This was taught using sine law if you recall Completed Snell’s Law With all our relationships in consideration Snell’s law can be expanded to the following. Important Pay close attention to the way this is formatted. The constants are inverted from the pattern of the formula. We will cover the reasons when we show proofs in the future for these formulas. Practice A ray of yellow light with a wavelength of 570 nm travels from air into diamond at an angle of 30 degrees. Determine: 1. The speed of light in the diamond 2. The wavelength of light in the diamond (n values from textbook for diamond are 2.42 and 1.00 for the diamond and air respectively) Prisms - An application of Refraction With our new Understanding of Snell’s Law we can now see how a prism can separate white light to its separate bands. As white light enters a prism it is refracted. Each wavelength of light bends at a slightly diﬀerent angle. This is called dispersion At the other side of a prism the light refracts again to its original speed and wavelength, however given that the individual wavelengths of light are now a distance apart the do not recombine to form white. When the colors are blended back together it is called recomposition Practice Textbook: Pg 668 and 670 Workbook: Page 204 - 210 (and all prior) SNAP: pg 153 - 168 (feel free to skip the lab if necessary) Internal reﬂection and Mirrors Refresher Questions to this point In Michelson’s last experiment he aimed to A 5.0cm object is placed 2.0cm in front of a measure the speed of light in a vacuum. He set up a converging mirror and the image is magniﬁed 4x. vacuum tube that was 1594.2658m long that would Where does the image form and what is the focal reﬂect the light over the distance 10 times. While length? the light reﬂected a 32 sided mirror would spin at a frequency of 587.60395 Hz. If the light came back in the time it took to rotate one side of the mirror what is the speed of light? How many sig ﬁgures to use in this question Refresher Questions A diverging mirror of focal length 10.0cm produces Light with a wavelength if 737nm enters quartz an image of an object located 20.0cm from the glass at an angle of 25.0 degrees, Determine the mirror. Determine the image distance and the angle of refraction and the wavelength of the light magniﬁcation. in the quartz glass. Is the image real or virtual n=1.47 in quartz glass Internal Reﬂection Recall: When light transitions from one medium to the next, some of it is reﬂected and some of it is refracted. New: When light moves from a slower medium (high index) to a faster medium (low index) MORE of the light is reﬂected than if it were to enter an even higher index medium. At some point, with the appropriate angle the light will cease to refract at all, and travel 90 degrees to the boundary. Internal Reﬂection Consider the diagram to the right. As the angle increases, so to does the refraction until it hits a point that the refracted angle is 90 degrees relative to the normal line. Any further increase to the angle generates something called internal reﬂection; where no light leaves whatsoever. Critical Angle The value of the incident angle that will generate a perfect 90 degree angle is called the critical angle. Consider: Snell’s Law, what is the value of sin(90)? Critical angle is important in many industries where escaping light can be a problem or aesthetic. Diamonds sparkle because their high refractive index and cut creates total internal reﬂection. Example problem What is the Critical Angle for the quartz glass - air interface? (table values state that nair=1.00 and n quartz = 1.47) Application The understanding of total internal reﬂection is used in ﬁbre optic cables. Fibre Optic cable has a composite glass ﬁlament center surrounding by a material with a lower refractive index. This structure means that all light sent through the cable remains in the glass ﬁlament, as it cannot reﬂect outwardly. Fibre Optic cable sends pulses of modulated light to code information, and given that it is light instead of electrons, it can travel faster and with less resistance. Lenses Thin Lenses Most lenses consist of a circular disk of material with a spherical shape through their width. Lenses are used in projectors, glasses, telescopes and many other forms of optic apparatus. There are two main types of lenses. Converging and Diverging Converging Lenses Converging lenses refract light moving parallel to a principal axis towards a focal point, or principal focus (F). Rays closer to the edge of a lense will be refracted to a greater degree than the rays closer to the center of a lens. The distance from the lens to F is a focal length (f) - Does this seem familiar? Diverging Lenses A diverging lens refracts light travelling parallel to the PA outward. The direction of the outward refraction can be thought of as a line extending outward from a virtual principal focus before the lens. This F is also an f away. 2 F’s Every lens has 2 locations for F. - The ﬁrst is in front of the lens and the other is behind. This is because lenses are transparent and can be used in either direction. - The second F is behind the lens. The value of each F is the same, however they are on opposite sides of the lens Center Rays In thin lenses it appears as though the center ray is not refracted. As it turns out it is refracted but only laterally (positionally) and by a small enough value that for our purposes we can assume it does not refract. Drawing Ray Diagrams for lenses Just as with Mirrors we will be drawing 3 rays with speciﬁc functions and rules to determine how the light will be aﬀected. This will also allow us to predict where an image will appear and how it will be aﬀected Lens Ray 1 The ﬁrst ray will be drawn from an object parallel to the PA. In a converging lens it will refract towards the principal focus In a diverging lens it will move away from the PA at an angle that would intersect with the virtual F Lens Ray 2 The second ray will be directed at the secondary focus. This is the F that is not being actively used. In a converging lens, this is the F before the lens, and in a diverging Lens this is the F after the lens. In both converging lens’ and diverging lens’ this ray is refracted to be parallel to the PA Lens Ray 3 The third ray for a Lens diagram travels directly through the center of a lens. As discussed earlier, this ray will not be refracted at all and will travel in a straight line. Describing images Just like in our conversations about Mirrors we can describe the image through a lens in terms of magnitude, attitude, position, and type. Let's quickly apply our mirror knowledge and new diagrams to describe some images Practice Using a converging lens, describe what a resulting object may look like if its initial position is at 1. Beyond 2f or C (very far away) 2. At the principal focus 3. Between F and the Lens Equations for Lenses Just like when we discuss mirrors, lenses generate similar right triangles throughout the path of their rays. A beautiful symmetry of nature allows us to ue the same equations that we used for mirrors on lenses. We may use formula 7 for the object Distance and formula 6 to describe The height. Sign Conventions of thin lens equations All distance measurements are relative to the center of the lens Positive distances are used for real objects and images Negative values are for virtual images Positive Image and object heights are upward relative to PA Negative Image and object heights are downward relative to PA Converging Lenses have a positive focal length Diverging lenses have a negative focal length. Practice Problem A 2.5 cm high object is placed 10.0 cm from a diverging lens of focal length 5.0cm Determine the image distance, height, and attributes using the thin lens equation. Practice Textbook: pg. 681 and 683 Workbook: Chapter 5 up to page 226 SNAP: up to page 205 Diffraction and Interference Physics 20 Understandings Interference: The eﬀect of two waves crossing within a medium; the resultant shape is diﬀerent than the shape of either wave on its own. Constructive interference: When two waves overlap to form a wave of greater amplitude (overall crest height) Destructive interference: When two waves overlap and create a wave of lesser amplitude. Physics 20 Phase and Standing waves In-Phase: Deﬁnes when waves crests and troughs occupy the same space in a medium (think lines up). Waves in phase form constructive interference Out-of-Phase: deﬁnes when a waves crests and troughs occupy opposing locations in a medium and form only destructive interference Standing wave: A condition in which a wave appears to oscillate around a single stationary point called a node. The wavelength of a standing wave is the distance between nodes. Wave Fronts Wave Front: A wavefront is a surface over which an optical wave has a constant phase. For example, When a stone is dropped in a still water, waves spread out along the surface of water in all directions with same velocity. Consider a Wave front to be an imaginary line drawn along all the area a wave touches at a given moment. Back to Physics 30 Christian Huygens (that dutch guy) is at it again with waves. He proposed the following idea regarding wavefronts “A wave front consists of many small point sources, of tiny waves called wavelets, which propagate outward in a concentric circle at the same speed as the wave itself. The line tangent to the wavelets constitutes the wave front” Let's discuss what this guy is talking about. Huygens Principle A model of wave theory which predicts the motion of a wave front as being many small point sources propagating outward in a concentric circle at the same speed as the wave itself. Diffraction According to Huygens Principle a wave front will continue to propagate in a straight line until it encounters a barrier. If the wave front encounters a small opening or aperture in the barrier, the wave will change shape and direction. This process is diﬀraction. Diffraction Diﬀraction: The change in shape and direction of a wave front as a result of encountering a small opening or aperture in a barrier or a corner. Problems with the Model Recall: Huygens theory is pretty solid, but at the time he was alive people were losing their minds over Newton. His Corpuscular (particle) model of light was gaining huge popularity. Thomas Young Proposed a an experiment that provided huge evidence for Huygens theories. The double slit experiment. The double slit take 2 Why the double slit Many physicists prior to young had attempted to show that light was a wave; and they tried to prove it by demonstrating wave interference with light. The problem was the design of previous physicists work; many attempts at generating interference did not take into account the extremely small wavelength of light and its proportionally high frequency, and the phase of the EMR. Previous Experiments Physicists prior tried using multiple light sources at varying distances to generate an interference pattern like the one shown below. The problem is that they used two diﬀerent light sources and to great of distance Diﬀerent light sources create diﬀerent wavelengths with diﬀerent phases. Diﬀerent phases means inconsistent interference patterns. The long Distance also caused issues with any interference pattern being strongly visible. Think about looking for your wave pattern 30 meters away in a Lake when you threw 2 diﬀerent sized stones in. It isn't eﬀective The double slit. Young avoided the issue of phase by using only a single light source. If the light came from the same source he could be sure that the phase and wavelength of all the incoming light was identical. Young generated the interference by splitting the light, eﬀectively creating two wave fronts. The result was ﬁnally an Interference pattern. *note youngs setup was not this fancy, He used a tiny pinhole of light that he split With a tiny piece of cardstock. Implications This is the ﬁrst irrefutable evidence for light acting as a wave. If light were simply a particle they would pass through the slits and cluster. Particles have no need to interfere with each others pathing. We see interference it must be waves right? Well, yeah, for now. Detractors and Science Drama People still preferred Newton’s explanation; as science can be a popularity contest sometimes. One detractor was a man named Poisson. Poisson used the equations that explain Thomas diﬀraction experiment and theorized that constructive interference would have a novel implication to a round disc. Poisson Theorized that there would be an area of constructive interference towards the center of an otherwise opaque disc’s shadow. Poisson’s theory Poisson theorized that a bright spot like to the right should form if the math was correct. He went about this research in an attempt to disprove Young’s work. He performed a weak experiment and could not ﬁnd the bright spot, and ﬁgured he refuted the wave model altogether. Domonique Argo Argo revisited poisson’s theory and was able to devise an experiment and actually could create the fabled bright spot of constructive interference. You can repeat this experiment with a round object and a laser pointer. Simple trial and error with distance can get yield a bright spot. Now: here is some A tier Science Shade. They named the spot after Poisson for being a jerk. Now for some math. The last conversation to have about this topic is to discuss the mathematics associated with predicting the interference pattern in a double slit experiment. Please consider the diagram posed below. This image highlights the key elements in any double slit or diﬀraction grating problem. We have displayed a light beam, a screen, a length (l) between the slit and screen, and a value of n. N represents the ﬁrst Node (or actually antinode in this case) from the central brightest line. Antinodes. Each Bright line, represents an antinode, which we represent with n. Antinodes are regions where constructive interference takes place. Between each antinode there is a node, where destructive interference takes place. The destructive interference yields no light at all as the wavelengths cancel. The distance between node and antinode is ½ a wavelength or ½ λ. The distance from node to node is 1λ Important Concerns Please be careful with calculations moving forward we are now using n to represent the node value, as well as refractive index. It is important to keep those separate as there is NO overlap in usages in our formulas. Because n in a double slit experiment counts a node we use only whole number values to describe it. We count nodes up 1 by one starting from the center point and counting up in either direction Formula 9 d sin θ = nλ This formula describes the relationship that exists between wavelength, the angle from a central line, the node number in question and the distance BETWEEN the slits In your formula sheet it is arranged as this Let's discuss d a bit further then solve some practice questions What is “d” “d” in the formula above represents how far apart he slits are. d is measured from the outside of one slit to the outside of the next slit. This can be used as a way to confuse students on test questions. PLEASE: when in doubt if you are using d correctly ask. I will happily tell you if there is more work to be done on a given question. However for the ﬁrst couple questions I will not be making it any more diﬃcult than it needs to be. Using Formula 9 (textbook question) Monochromatic light is incident on two slits separated by a distance of 0.30mm, and the ﬁrst bright fringe (n=1 antinode) is located at an angle of 0.080 degrees from the central antinode. What is the wavelength of light? Diﬃculty enhancers: - Wordings: terms like bright fringe, antinodal line can mean the same thing, much like nodal line, interference line, or dark fringe can mean the nodes (dark space). - Distance: I can make you do some basic maths to ﬁnd the distance in a scenario - Trigonometry: I can give you a distance on the screen and a length and make you use trig to solve for the angle. Formula 10 The double slit experiment can also be calculated using the 10th formula on the sheet. In this formula we are introduced to x, and l. L was described in an earlier slide X = the distance between any given node or antinode and the next node or antinode Practice Problem A student measuring the wavelength of light emitted by a krypton gas sample directs its light through two slits separated by 0.264mm. An interference pattern is created on a screen 3.0m from the slits and the distance between the second bright fringe and the central bright spot was measured to be 1.18 cm. What is one of the wavelengths of light emitted by the krypton gas sample? When to use Generally speaking the tenth formula is used when the angle is small enough that the tangent and sine of an angle are almost identical. To ensure the best results on exams and assessments try to limit use of the 10th formula to scenarios when the angle of deviation from the central line is 10 degrees or less. Why have 2 formulas then? It is really hard to measure the angle in a lab scenario especially given the tools available. So the 10th formula is really handy for measuring. Diffraction Gratings Diffraction Gratings Diﬀraction gratings are a series of very small slits that are aligned on a material. Consider a piece of of clear plastic with hundreds or even thousands of parallel lines scratched into the surface. We use diﬀraction gratings to allow more light to pass, yielding sharper stronger images. Relationships A diﬀraction grating scales with the number of slits. The more slits the more destructive and constructive interference. The bright spots become brighter and wider and so fo the dark fringes. Diﬀraction gratings also happen to split visible light into its separate colors of the rainbow. Important A diﬀraction Grating splits white light into its baser wavelengths(colors); and you may assume this is similar to a prism. It is important to remember that the color ordering is the opposite to a prism as we are using diﬀraction and not refraction Prism: Blue Refracts the most, and Red the least Diﬀraction Grating: Red undergoes the diﬀraction, blue the least Unit Analysis on Diffraction Gratings A diﬀraction grating has an issue. The value of d is hard to calculate as we no longer have just two slits to work with! Consider a grating that has 600 lines/mm. Is there a way we can make this into a unit of distance instead of a unit per distance? Inverse We can take the inverse value of the grating. By using the inverse value we can now that number as d Practice Question A CDROM acts as a diffraction grating as it reflects light since it has many small imprints lined up as a way of storing data. An experiment is performed to determine the line spacing on a CDROM using a pocket laser pointer. The following data was recorded: wavelength of laser pointer: 680 nm distance from the screen to the CDROM: 94.0 cm distance from the bright central max to the first maximum: 42.5 cm a. Determine the spacing of the lines on the CDROM. (Hint: is the angle greater than 10°?) b. How many lines per mm is the CD rom Dispersion and Polarization Dispersion Recall: We described dispersion previously as the process by which light seperates in a prism. Given time constraints we simply stated this happens due to refraction, and while this is true it is important that we visit this topic with greater detail, prior to starting the next chapter. Dispersion Recall: The reason light seperates in a prism is because each wavelength will bend a diﬀerent amount, and change velocity by a diﬀerent amount in a given substance. Let's Explain that with a meme. Do you remember double rainbow? If not, here Rainbows Rainbows are produced due to the differing refractive indexes of sunlight through million of water droplets. Using our understanding of internal reﬂection and refraction we can trace the lights path in a water droplet Requirements for a rainbow with this diagram In the situation shown the sun must be coming from behind the observer, and hit at the precise right angle to allow internal reﬂection. If the angle is oﬀ the light will pass through and not be refracted far enough to project the component colors of light. But what about double rainbows? More intense? Double Rainbows Double rainbows happen when the initial angle allows for longer internal reﬂection. The longer the light is trapped the further it can refract and be emitted. Double rainbows are interesting because the order of colors is reversed! Thought. Why are double rainbows so much dimmer than a primary rainbow? Polarization Recall: When we started this unit I demonstrated a strange phenomena with two lenses. Let's review this demonstration with the video below. (0-1 minute) VIDEO Polarization is one of the strongest proofs regarding the wave nature of Light. If light is a transverse wave (shown below) then it will appear with a variety of orientations. For the sake of discussion we will provide two orientations. Polarized Lenses If we are to consider the orientation of the Electromagnetic wave to be in either a vertical or horizontal orientation we set up unique ﬁlters for that light. If light is transversal it will be blocked by the ﬁlter, if it is not a transverse wave then it will pass through ﬁlters unaﬀected. As seen at the top of the unit light clearly can act as a transverse wave. Polarization There are no expected calculations in regards to polarization of light. Though it should be known that a 90 degree turn of a polarized lens will generally reduce the passing light by approximately 50%. Extension question: Why is this a generality and not a hard and fast rule? Polarization Polarization is generally accepted as some of the strongest evidence for the wave model of light. This is the end of everything in Chapter 13. Please ensure you have read the chapter as we move forward to 14. Textbook: 699-701 Workbook: up to 247 Snap: Up to 232 Review Review Questions (Nature of Light, Speed of Light) - How is EMR generated? - Light is reﬂected from an 8 sided set of rotating mirrors (michelson experiment) - What area of the EMR spectrum would you travels 15 km to a ﬁxed mirror and then expect to ﬁnd a wave with a wavelength of travels back to be viewed by an observer in 7.5x10-7m the time it takes for the mirror to turn 1/8th of a rotation. What is the frequency of the - Draw a model of an EMR wave apparatus - A sample of light was found to have a - wavelength of 8.6x10-12m; what is its frequency in a vacuum. - Is this high energy radiation? Review Questions (Mirrors, and Lenses) - A 25 cm tall object is 50 cm from a convex - A 6.5cm high object is 15cm from a concave lens with a focal point that is twice the mirror with a 20.0cm radius. Determine the distance of the objects height. Will there be a image distance and image size. visible image? Describe - A 5.0cm tall object is placed 4.0cm in front of - The cornea of a human eye acts as a a mirror having a focal length of -6.0cm. converging lens. An eye with a radius of Identify: curvature 8.5mm views an object that is 2m - The type of mirror used away, and 1.5m tall. Describe the image and - The image characteristics - The Image distance state its size in the eye. - The Size of the image produced Review Questions (Refraction) End for Quiz - State a relationship between the index of - The speed of light in a clear liquid is three refraction of a material and the speed of light quarters the speed of light in air; Determine the critical angle of the liquid. - Determine the refractive index of a substance where light travels at 2.45x108 - Describe what happens when the angle of - A green laser with a wavelength of 532 nm is the incident ray is greater than than the commonplace tool for scientists and kids critical angle? alike. Determine the speed of the laser in transparent plastic if its wavelength refracts to 480nm in plastic. Things you have to know The list to the right contains all the information that you are expected to have memorized or general knowledge of. Anything else you will be provided new information for. Practice Textbook: Page 689, 691, and 697 Workbook: Page 237 to extensions. We are brieﬂy skipping section 229-234 SNAP: read 205 and do 217 - 220

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