DLM07_stu

DLM07_stu - Physics 7C DLM07 Overview DLM 07 Model:...

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Unformatted text preview: Physics 7C DLM07 Overview DLM 07 Model: Standing Waves Act 8.5.4 Standing Wave Wrap-up (FNT’S) (~40 min) Learning Goals: - See DLM06 for Learning goals Model: Ray Optics Act 8.6.1 Wavefronts, Rays, and Refraction (~20 min) Learning Goals: ~ Understand the connection between the “ray representation” of a wave and the “wavefront representation of the same wave”. - Understand why a change in wave speed can lead to a change in direction for a wave in 2 or 3 dimensions Act 8.6.2 The Law of Reflection (~20 min) Learning Goals: ~ Recognize that light is a type of harmonic wave with a wide range of frequencies, traveling at the speed c = 3.00 X 108 m/s in a vacuum, and at speed v = c/n in “transparent” media, where n is the index of refraction, a constant characteristic of the medium in question ~ Understand that light reflects from the boundary or interface between two “transparent” media in such a way that the angle of incidence equals the angle of reflection Act 8.6.3 The Law of Refraction (~50 min) Learning Goals: - Understand that light propagating from one “transparent” medium into another will, in general, refract or bend from its initial path in accordance with the law of refraction - Investigate total internal reflection: when light propagates from an “optically-dense” material to a less “optically-dense” material, there is a minimum value of incident angle (i.e., the critical angle) for which the wave is completely reflected - Investigate the bending of light as it passes through a prism via the law of refraction ~ Use the geometrical properties of simple prisms to model lenses, both with converging or diverging focal points (i.e., convergent or divergent lenses, respectively). Physics 7C Activity 8.5.4 DLM 07 Standing Wave Wrap-up A) Mastering one FNT Your TA will assign you one of the following: FNT 1), 2), 3)a), or 3)b). 1) As a group, determine an ideal solution to the FNT and write this solution on the board. 2) As a group, determine how you will teach this FNT to the class. Appoint two group representatives to teach the class, and do a practice run-through. 3) With remaining time, compare answers and gather questions you have about the FNTs you are not assigned to teach to the class. Whole Class Discussion B) Making connections 1) Now that you have seen a solution to each FNT, compare the FNTs to one another. Identify the concepts you learned in this activity that proved problematic to you at home. Write these concepts on the board. 2) Make certain you could teach the class any of these FNTs, not just the one you did in detail in part A. Whole Class Discussion Physics 7C Activity 8.6.1 DLM 07 Wavefronts, Rays, and Refraction When a wave passing through some medium comes to an interface with another medium the energy of this wave is divided between two waves: i) a reflected wave carries some of the wave energy back into the original medium and ii) a refracted wave carries the rest of the energy through the new medium. We will talk first about the refracted wave. A) Mud-marching model of refraction 1) Think of our wavefront model of a wave as a marching band arranged in perfect rows and marching on a football field. A schematic picture of the band (as viewed from above) is shown to the right. The band is marchng to the right. In the middle of the field there is an interface separating the dry side of the field from Dry Side of field Muddy Side offield the muddy side of the field. The mud slows down the band so that their speed in the mud is only 1/2 what it was on the dry side. On the board sketch a picture of the band when three rows of the band is in the mud and the rest are still on the dry side. Sketch the appropriate rays for the incident wave (the band in the dry side of the field) and the refracted wave (the band in the mud side of the field). 2) Now we consider a field that has an interface at an Muddy side of field angle as shown to the right. We can do an experiment to figure out what will happen. Your TA will help you set up the experiment but everyone has to go outside to perform the experiment. After the experiment, you should understand what happens to the band as it crosses into the muddy side. Again, sketch a picture of the band when half the band has crossed into the mud side and half is still on the dry side. Sketch the appropriate rays for the incident wave (dry side) and the refracted wave (muddy side). Dry side of field 3) The picture to the right shows a prism made out of clear acrylic Prism plastic. It turns out that lightwaves move more slowly in the plastic than in air. On the board, sketch this picture and then sketch in a reasonable refracted ray (i.e. the light ray inside the prism). B) Snell’s Law incident | / \ B ./‘ 1 / In a vacuum (or in air), light travels at the famous “speed of light” Normal \.\/' c = 3.00 X 108 m/s (this is about 671 million miles per hour!). (perpendicular to Light travels through matter, such as window glass or water, at air/prism SUFfaCE) speeds, v, that are slower than c. For “transparent” materials, we can define a quantity called the index of refraction, “n,” to compare these speeds, such that n = c/v Since v in such materials is less than c, n must necessarily have a value greater than unity. Snell’s Law of Refraction: nlsinel = nzsinez - “1” and “2” denote the two media - n1 and n2 are the indices of refraction o 91 and 92 are the angles the light beam makes with the normal at the interface. How does Snell’s Law explain what you saw displayed by the marching band model? Whole Class Discussion Physics 7C Activity 8.6.2 DLM 07 The Law of Reflection The Law of Reflection dictates how an incident light ray will reflect from the interface between two media. Specifically, the angle of incidence Bitumen“, (a.k.a. 9i) as measured from the imaginary line perpendicular to interface at the point where the light ray hits (called the normal line), is equal to the angle of reflection ereflection; (a.k.a. 0r): “LBW” 0f Reflection: Hincidence = (inflection This “law” is evident to anyone who has shined a laser pointer onto a mirrored surface and analogous to a billiard ball reflecting of a tableside. Note: It is called a “law” for historical reasons, but simply describes what happens when the reflecting surface is smooth compared to the wavelength of the wave. For example, the “law” does “not hold” when light hits a common piece of white paper! In your table groups: 1) Set up the light source and rotating protractor platform as illustrated (see figure below). Place the semi-circular acrylic (a common form of plastic) prism on the protractor platform — since the angles of incidence and reflection are measured with respect to the normal to the flat surface of the plastic block, what orientation of the block on the protractor platform will make the angle measurements easiest? 2) Confirm and demonstrate the Law of Reflection. Be prepared to define each parameter in this equation with respect to this experimental apparatus. 3) The upcoming activity requires you to use this setup to make some precise angular measurements. Use the Law of Reflection to calibrate this equipment so that you can make accurate angular measurements. Be prepared to demonstrate how to do this. (w: This will require you to adjust the laser position, the rotation of the protractor, and the position of the acrylic prism.) Proper calibration requires: a. The “line” of light should be straight in the middle of the protractor (0°) with the prism removed. b. 9i = 0r for all angles less than 900 as viewed on the protractor c. With the light beam at 00 to the prism surface, the transmitted beam (the beam that goes completely through the prism) should continue straight. 4) Compare the relative intensity of the reflected beam as a function of angle of incidence. Is the reflectance a function of angle? Explain the dependence, if any, in terms of the reflected as well as the transmitted light rays. EXTRA TIME? If you have extra time, wrap the prism in paper and discuss the difference in the type of reflection you see. Without the paper, you get specular reflection. With the paper, it is diffuse. acrylic prism cylindrical incident He/Ne laser rotating platform reflected Whole Class Discussion Fay Physics 7C Activity 8.6.3 DLM 07 The “Law” of Refraction A) Refraction Measurements In your table groups: 1) Set up the apparatus as shown in the figure below, with the light beam going into the flat side of the acrylic prism. Take whatever measurements necessary to determine the speed of light in acrylic. Note that the speed of light in air Va], is nearly the vacuum value c = 3.00 X 108 m/s. Refraction, air to acrylic (top Rcfiacfion, acrylic to air (top View) View) 2) Look at the two figures above. Explain how one setup will allow you to measure the refraction from acrylic to air, and the other will allow you to measure the refraction from air to acrylic. In each orientation there are two interfaces, why does one of the interfaces not matter? Whole Class Discussion 3) Repeat part 1) with the light beam going into the curved side. Keep the angle of incidence Bacryhc relatively small (e.g., 250). Verify using The Law of Refraction that you obtain the same index of refraction for acrylic. (If time is short, your TA may ask you to record data, and verify the index of refraction at home). 4) Observe whether the angle Gwyn-c of the incident ray is bigger or smaller than the angle Bar of the refracted ray. Explain whether this is consistent with the law of refraction. 5) Use the mud-marching model to create a general rule (non-numerical rule) that relates the incident angle to the refracted angle when a light ray is transmitted into a slower medium and a faster medium (i.e. Does the ray bend toward or away from the normal in each case?) Continued on other side Physics 7C Activity 8.6.3 DLM 07 6) For the configuration of Question 3), slowly increase 0mm until you get to about 50°. You will observe an odd effect. What happens differently when Gacryhc approaches 50°? Explain whether this is consistent with the law of refraction. What does the mud-marching model tells us about what is happening here? Ask your TA what this is called or look at your Course Notes. 7) From your observations in Question 5), precisely determine the incident angle 0mm at which this phenomenon occurs — we will call this the critical angle 9mm. Also record the exact angle flair of the refracted ray (i.e., the one exiting out into air) when 9m.th = 63mm. 8) Use the law of refraction to calculate 8mm of acrylic. Whole Class Discussion B) Light through plastic shapes: Refraction at two interfaces If your class finishes this Part B, you may skip FNT 1 On the board, make a large, accurate sketch of an equilateral triangle (such as shown to the right) and draw the incoming horizontal light ray as shown to the right. Suppose this triangle is the cross-section of a plastic prism. Use the mud-marching model and/or the law of refraction to sketch the path of this ray inside the prism and then the path of the ray to the right of this prism. incoming ray Plastic prism n = 1.5 Physics 7C FNTS DLM 07 Model: Ray Optics 0) Look at Activity 8.6.3. If you did not finish the activity in DL, do so for homework. This may include Questions 3, 4, 5, and Part B. 1) (Solidification) Make a large, accurate sketch of an equilateral triangle (such as shown to the right) and draw the incoming horizontal light ray as shown to the right. Suppose this triangle is the cross-section of a plastic prism. Use the mud-marching model and/or the law of refraction to sketch the path of this ray inside the prism and then the path of the ray to the right of this prism. incoming ray Plastic prism n = 1.5 2) (Application) Sketch the three structures shown below on the board and, for each one separately, show how the three parallel incident light rays bend as they pass through the plastic prism and out the other side. Describe in words what each of these structures does to parallel light rays using the word “focus” as necessary. Which of these shapes would be better for starting a fire with sunlight? —> —> —> ' —> —> —> —> —> 3) (Application) A fiber optic wire uses total internal reflection to transmit light down the wire. It is constructed from two types of glass, with indices of refraction n1 = 1.45 and 112 = 1.52. A glass filament forms the core of the wire, with a cladding of the other glass type wrapped around it. (a) Which glass forms the core, Cladding and which forms the cladding? we Briefly justify your answer. (b) What is the minimum incident angle a light ray originating from end View cross section within the core can strike the core/cladding boundary and not be transmitted through it at all? 4) (Introduction) If you haven’t already, download the course notes. Read section 8-3-3-1, “Ray tracing: using the principal rays.” You will need to have read this section in order to complete FNT 5. 5) Complete the ten ray tracings for the converging and diverging lenses on the pages provided during this DL Meeting. Use a ruler or straightedge to draw the representative principal light rays. It may take you a little while to get started, but once you understand the principal rays for each lens type, it will go fast! The instructions on the following pages are incomplete. You must read 8—3-3-1! Physics 7C FNTS DLM 07 Converging Lens Ray Tracings — You can always draw the following three rays that come from the top of the object and pass through the lens (we call these three, the “principal rays”): 1. Straight through the middle. 2. Parallel to axis, then through the far f. 3. Through the near f, then parallel to axis. (or from near f to object, then parallel) (a) Far away from f A (C) On 7‘ A object (d) Inside 2‘ A (e) Near lens A Physics 7C FNTS DLM 07 Diverging Lens Ray Tracings — You can always draw the following three rays that come from the top of the object and pass through the lens (we call these three, the “principal rays”): 1. Straight through the middle. 2. Parallel to axis, then away from the near f. 3. Toward the far f, then parallel to axis. (a) Far away from f (d) Inside 2‘ (e) Near lens ...
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This note was uploaded on 04/22/2011 for the course PHY 7C taught by Professor Mahmud during the Spring '08 term at UC Davis.

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DLM07_stu - Physics 7C DLM07 Overview DLM 07 Model:...

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