LAB REFLECTION FROM A PLANE MIRROR

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1 Name (printed) LAB REFLETION FROM A PLANE MIRROR W E LOVE TO look at plane mirrors. We look at them as we enter and leave bathrooms. At the gym we work out in ront o them. We can t help taking a quick look at the mirrored walls o elevators. But let s be honest. It s not the mirror we re looking at. No, we re really looking at ourselves! (Well technically, we re looking at images o ourselves.) The storeront windows o businesses act well enough as plane mirrors that we use them to check ourselves out while we pretend that we re looking through them at merchandise. We love to look at ourselves and because o this, it s hard to ind places where there are no mirrors. To make sure we can always get an image ix we carry them in our purses and backpacks. I m sure that our prehistoric ancestors were probably just as ixated by the images they saw o themselves in lat pools o water. We use plane mirrors more oten than curved mirrors because plane mirrors produce images that are the best representation o ourselves. The image produced by a plane mirror is identical in size and orientation to its object. On the other hand, curved mirrors (concave and convex) produce images that are sometimes larger, sometimes smaller, and sometimes upside down. What is it about plane mirrors that causes them to produce so identical an image? Answering that is one o the goals or this lab. Starting with plane mirrors is a great way to start thinking about optics (and about physics in general). It s easy to make some simple measurements that lead directly to some general rules (aka laws o nature ). It s true that plane mirrors produce simpler images than curved mirrors, but they certainly aren t trivial. Ask a group o people who have never studied optics where they think the image produced by a plane mirror is located and you ll get three responses. Some will say, On the mirror surace, o course. Others will say, In ront o the mirror s surace, o course. Still others will say, Behind the mirror s surace, o course. People tend to be emphatic about what they know to be true. But all three locations can t be right. This lab will lead you to the discovery o this image position. More important will be the discovery o two laws o relection, one o which is a universal rule that applies to all relections, not just those rom lat suraces. The image produced by a plane mirror gives the best representation o an object. The image size and orientation are identical to the object. (an you tell that there is only hal a house o cards?) Photo by Haydn Wall, lass o In the space below, write down where you think the image produced by a plane mirror is located. Include some explanation or evidence or your answer (even i it s just your intuition). 1

2 PURPOSE To become acquainted with the qualitative and quantitative relationships which exist between the object and its corresponding image in a plane mirror. Speciically, you will discover: - the position o the image with respect to the object. - the relationship between the angle o incidence and the angle o relection. PROEDURE: 1. Place the sheet labeled Part A o the lab on the piece o cardboard. 2. Place the mirror with the attached wooden block on the line marked mirror, so that the relective side is lush with the paper and aces the point marked Object. These are rear-suraced mirrors so the backside o the mirror should be on the line marked mirror. 3. Place a lorist pin (it has a little ball on top) on the point marked Object. 4. Place the two regular pins on the points 1 and 1a. Make sure all pins are vertical. 5. With your eye at table level look at the two regular pins at points 1 and 1a and note how these pins line up with the image o the lorist pin. Be absolutely sure each person sees this alignment beore you go on. It s a lot like looking (rom end view) at three people all standing in a line, and only seeing the irst person because the other two are exactly behind that irst person. 6. Look into the mirror rom a viewpoint well to the right o the object. Place the two regular pins so that they line up with the image o the lorist pin as beore. Label these points 2 and 2a. 7. Repeat this or a third angle, on the right or let side. Label these points 3 and 3a. 8. For each o the three sets o points, draw a dashed line representing the path that light appears to be traveling rom the image to the eye. The irst one is done or you already. 9. Use these lines to identiy the image position, and label that point image. 10. For each o the three pairs o points (1/1a, 2/2a, 3/3a), draw a solid line representing the path that light actually takes as it goes rom the object to the mirror to the eye. 11. Draw arrows on all light rays indicating the direction o actual and apparent light. See diagrams. 12. Draw normal lines (right angle) to the mirror at each point where the solid lines touch the mirror. 13. Measure and record the angles o incidence and the angles o relection. incident ray normal line incident relected angle angle q relected i q r ray relective surace Ray diagrams lines mirror actual ray apparent ray normal line 2

3 DATA & ANALYSIS 1. The apparent path length o light is the path that light seems to travel according to our eye. In centimeters, measure and record the apparent path length o light rom the image to the eye. Sighting Incident Angle Relected Angle Apparent path length Actual path length 2. The actual path length o light is the path that light really travels rom an object to our eye. In centimeters, measure and record the actual path length o light rom the object to the mirror to the eye The object distance is measured rom the object perpendicularly to the mirror. In centimeters, measure and record the object distance. 4. The image distance is measured rom the image perpendicularly to the mirror. In centimeters, measure and record the image distance. Object Distance: Image Distance: Mirror 1 1a Eye Object Part A 3 Move ahead 100% ORRET

4 QUESTIONS 1. Summarize your observations about the behavior o light as it strikes a plane mirror (this should include statements both about incident vs. relected angles as well as apparent vs. actual path lengths. 2. Explain (and draw a picture) how plane mirrors put on walls can make rooms look larger. 3. The astronauts put a corner-relecting mirror on the moon. This is a combination o mirrors that are joined at 90 angles like the photo to the right (taken by David Angelo and Michael Barbaro, lass o 2004). The mirrors on the moon are designed to relect laser beams sent rom the Earth directly back along a line parallel to the path they came on. The perpendicular lines below represent two plane mirrors at right angles. Draw normals (I drew the irst or you) in order to measure and draw angles. omplete the drawing and then bring in another incident ray in a direction that is dierent rom the irst, again completing the path, in order to illustrate this property o corner relectors. 4

5 4. The cat below is sitting in ront o a plane mirror. areully ollow the ollowing instructions in order to show how the cat s image is ormed by the plane mirror. a. Draw two rays rom the tip o the ear o the cat to the mirror and two rays rom the tip o the paw o the cat to the mirror. b. Draw normals at each o the our point where the rays intersect the mirror. c. Use the law o relection to draw the our relected rays. d. Trace each o the relected rays back behind the mirror (these should be dashed lines since they are only apparent paths. e. Indicate the positions o the images o the cat s ear and paw at the point where the apparent paths appear to converge (or emerge rom). Plane Mirror 5 Move ahead 100% ORRET

6 INTRODUTION TO URVED MIRRORS urved spherical mirrors are sections o relective spheres. oncave mirrors come rom the inside o the sphere and convex mirrors come rom the outside o the sphere What is the center o curvature or radius o curvature? Physics o a concave mirror Headlight Physics What is the ocal point? 6

7 ATIVITY MIRROR RAY DIAGRAMS PROEDURE In the drawings on this and the ollowing pages, the arrows represent objects in ront o either concave or convex mirrors. Make ray diagrams to locate the corresponding images. Draw in the complete image as an arrow. For each image arrow, indicate the: - Location o the image, L (behind mirror, between and, at, beyond ) - Orientation o the image arrow, compared to the object arrow, O (upright or inverted) - Relative size o image compared to the object arrow, S (smaller, same, larger) - Type, T (real or virtual) L O S T L O S T L O S T 7

8 L O S T L O S T L O S T 8

9 L O S T L O S T L O S T 9 Move ahead 100% ORRET

10 LAB REFLETION FROM A URVED MIRROR INTRODUTION TO PART 1 Images produced by mirrors can be deined according to their style. Style reers to our particular qualities o the image: its distance rom the mirror (compared to the object), its size (compared to the object), its orientation (compared to the object), and its type (real or a virtual image). Plane mirror images are simplistic they always have the same style. Wherever you put the object, the image is always the same distance behind the mirror as the object is in ront, always the same size as the object, always upright, and always virtual. urved mirrors (concave or convex) produce images with much more variety. The image produced by a curved mirror can be closer to, arther away, or even the same distance rom the mirror as the object. The image can be larger, smaller, or the same size. It can be the same orientation as the object or inverted. Finally, curved mirror images can be either real or virtual. So with all these options, it might seem impossible to look at curved mirror images with any sense o order and simplicity. However, it turns out that with concave mirrors there are only our dierent styles o images. The style changes when the object moves rom region to region in ront o the mirror. The most important goal o this lab is to discover these our styles and understand what the rationale or the regions that they occur in. PROEDURE (PART 1) 1. Place the light bulb on the table so that all parts o the ilament are the same distance rom the relecting portion o the mirror (these are ront-surace mirrors, so please don t touch the relecting surace). Then use a 3 x 5 card to catch the image. This can be a bit diicult at irst and takes a bit o practice. (It can also be impossible. Remember, i the image being produced is virtual, it cannot be projected onto the card and will instead be behind the mirror.) 2. Practice moving the light bulb closer to and arther rom the mirror until you get good at predicting what the image will do. When you eel like you ve got the hang o this, complete the statements below. When comparing size use smaller, larger, or same size. When comparing orientation use upright or inverted. a. When the image has a greater distance rom the mirror than the object (light bulb ilament), the image size is than the object and its orientation is. b. When the image has a smaller distance rom the mirror than the object, the image size is than the object and its orientation is. c. When the image has the same distance rom the mirror as the object, the image size is than the object and its orientation is. 3. There is a pattern between the image distance and the image size (compared to the object). What is that pattern? 4. So ar, all the images you ve produced are real images (you were able to project them onto the card). Now get the object very close to the mirror. You ll produce a virtual image that you will need to look into the mirror to see. Looking at the image, you should be able to see two undamental dierences between this virtual image and the real images you produced earlier. What are these two dierences? 10 Move ahead 100% ORRET

11 REFLETION FROM A URVED MIRROR (ONTINUED) INTRODUTION TO PARTS 2 AND 3 I you don t like math, it s probably because you learned it in a math class. The problem with learning math in a math class is that it s typically taught and learned out o context. Take calculus, or example. Many o you are taking that class this year. You ll learn lots o rules and methods and techniques. But calculus had one purpose when it was invented. Isaac Newton developed calculus because he needed it to understand the physics o gravity. That s it! Math is a language, much like the languages you might be learning in the World Language Department. Nature speaks math. She will communicate with you and even give up her ways and her secrets, but only through math. So don t be a math-hater. We won t be using super-sophisticated math in this class and when we use math, it will never be or math s sake. Instead, we will use math to communicate with nature. So let s see how that works. We ll start with this:. That s the mirror equation, where 1 = 1 d o + 1 d i is the ocal length d o is the distance an object is rom the mirror d i is the distance the image is rom the mirror What nature is saying with this mathematical equation is that there is a speciic relationship between the ocal length o a mirror, the distance an object is placed in ront o that mirror, and the position where the image will orm. I the object is moved, the equation will speciy where the new image position will be. You can use algebra to express the mirror equation as: = d od i d o +d i. In this orm, it is easy to measure an object distance and an image distance and then calculate what the ocal length must be. That s the next goal o the lab determine the ocal length o your mirror. As you did in Part 1, you ll use the same light bulb ilament and 3 x 5 card as your object and image. A inal goal o the lab is to link what you did in Part 1 with what you do in Part 2. As mentioned beore, there are our dierent styles o images that can be produced by a concave mirror. The style changes when the object moves rom region to region in ront o the mirror. The object regions are: 1. Between the mirror and the ocus,. 2. Between the ocus and the center o curvature,. 3. At. 4. Beyond. Your job is to establish the style o image produced when the object is within each o these regions. PURPOSE To become amiliar with the nature o the images ormed by a concave mirror. Speciically, you will discover: 1. How to determine the ocal length o a curved mirror 2. What the style o the image is (position, type, orientation, and relative size) when the object is in the ollowing positions: between the mirror and the ocus,, between the ocus and the center o curvature,, at, and beyond. di do Figure 1: Set up or collecting real image data. Be careul to make measurements to the ilament o the light bulb, rather than the glass part o the bulb. Figure 2: Real Image projected on card 10

12 PROEDURE (PART 2) 1. Tape down a piece o white ticker tape approximately 1.5 meters long. 2. Place the mirror at one end on a piece o clay. 3. Direct the relecting portion o the mirror directly down the ticker tape. Make a mark on the tape to indicate where the relective surace o the mirror is. (These are ront-surace mirrors.) 4. Place the light bulb on the table so that all parts o the ilament are the same distance rom the mirror. Then use a 3 x 5 card to catch the image (see Figures 1 and 2). You can mark the object and image positions directly on the tape and then measure them later. Do this or at least ive object positions (two where the object is closer to the mirror than the image, two where it is arther rom the mirror than the image, and one where the object and image are at the same location). 5. Make a neat data table below. Use a straightedge and label the columns careully. Record the object and image distances as well as the calculated ocal length. I the precision o your ocal length calculations is poor, keep taking data until it improves. It is reasonable to throw out obvious outliers beore you calculate the average ocal length. DATA AND ALULATIONS Mirror size (circle one): Small Large 6. alculate the average ocal length and center o curvature. Average ocal length, = enter o curvature, = 11 Move ahead 100% ORRET

13 PROEDURE (PART 3) 1. Turn your ticker tape over so that there are no markings on it. Mark the tape again where the surace o the mirror will be. Measure out rom the mirror position and mark where the ocal length and the center o curvature are. 2. Now use your light bulb to test the style o the image produced by a curved mirror or each o the object positions indicated (with the exception o the region between the mirror and the ocus). For the object position between the mirror and the ocus, use a pencil as the object and peer into the mirror, comparing the image o the pencil to the actual pencil. Use the table below to describe the image. The possible entries or the table are shown in parentheses below. Image location: (behind mirror, between mirror and, between and, at, beyond ) Image orientation: (upright or inverted) Image size: (larger, smaller, or same) Image type: (real or virtual) Object Position oncave Mirror Images Position Size Orientation Type Mirror F F Beyond 3. State how the image size changes when the object moves within (not between) each o the ollowing positions: a. From the mirror to the ocus. b. From the ocus to the center o curvature. c. Beyond the center o curvature. 4. The tables below are like the one that appears above. These are or the much simpler plane and convex mirrors (which each only have one style o image). Use what you know about or observe in these kinds mirrors to ill in the tables using the same descriptors as you used in the table above. Object Position Plane Mirror Images Position Size Orientation Type Anywhere Object Position onvex Mirror Images Position Size Orientation Type Anywhere 12 Move ahead 100% ORRET

14 Use the tables you created on the previous page to answer the next questions. 5. The distance o an object rom a concave mirror is varied until both object and image distances are 100 cm rom the mirror. What is the ocal length o the mirror? a. 50 cm b 100 cm c. 150 cm d. 200 cm 6. A concave mirror has a center o curvature o 20 cm. For which object distance will the image be real, inverted and larger than the object? a. 5 cm b. 10 cm c. 15 cm d. 28 cm 7. The distance o an object rom a concave mirror is varied until both object and image distances are 50 cm rom the mirror. How does the size o the image compare to the size o the object when the object is moved out to 65 cm rom the mirror? a. smaller than the object b. same size as the object c. larger than the object 8. I you wanted to use the mirror in the previous question to help you to apply makeup, where would you place your ace in order to use it as it is intended to be used (that is, upright and magniied)? a. less than 25 cm b. 25 cm 50 cm c. 50 cm d. > 50 cm 9. You pull the bowl o a spoon closer and closer to your eye and notice that the image o your eye lips right side up when the spoon is 2.0 cm away. How ar would you put a candle lame away rom the spoon i you wanted to make the largest possible image o the lame out in ront o the spoon on a wall? a. less than, but very close to 2.0 cm c. less than, but very close to 4.0 cm b. greater than, but very close to 2.0 cm d. greater than, but very close to 4.0 cm 10. The table below lists object and image distances or objects in ront o six dierent mirrors. Identiy each type o mirror? Object Distance (cm) Image Distance (cm) Type o Mirror (Plane, oncave, onvex, or None) Reason or choice 13 Move ahead 100% ORRET

15 USING THE MIRROR EQUATION 1 or or or M = h i = = d od i d d h o o d o = d i d i = d o i d o + d i d i - d o - M = d i d o Focal Length onventions: oncave Mirrors onvex Mirrors Image Distance onventions Image in ront o mirror Image behind mirror The interesting connection between image size compared to object size and image distance compared to object distance: 1. A girl is using a concave makeup mirror to get ready or the Prom and is 27 cm in ront o the mirror. The image is 65 cm behind the mirror. a. Find the ocal length o the mirror. b. Find the magniication o her image. 2. The image produced by a concave mirror is 83 cm behind the mirror. I the mirror has a ocal length o 35 cm, where is the object? 3. A convex mirror has a center o curvature o 68 cm. I the image is located 22 cm rom the mirror, where is the object? 14

16 Do these three on your own and get checked when you are inished. 1. A concave mirror is designed so the virtual image is our times the size o the object when the distance between the object and the mirror is 18 cm. What is the center o curvature o the mirror? Given: 2. A convex security mirror in a department store has a center o curvature o 4.0 m. I a 1.6 m tall customer is standing 15 m in ront o the mirror, how tall is her image? Given: 3. An object is 1.0 m in ront o a mirror. A virtual image is ormed 10 m behind the mirror. What is the center o curvature o the mirror? Given: 15 Move ahead 100% ORRET

17 MIRROR EQUATION PROBLEM SOLVING In the space below, do the ollowing problems rom the Giancoli book: Pages , problems 9, 10, 11, 14, 20, 91 Start each problem with givens (like I taught you) and show all work. 1. A concave shaving mirror has a ocal length o 12.5 cm. For each o the ollowing cases, ind the image distance, magniication, and use sign conventions to explain i the image is real or virtual and upright or inverted. a. Object located 45.0 cm rom the mirror. b. Object located 10.0 cm rom the mirror. 2. A dentist uses a small mirror to magniy a tooth. When it is held 2.20 cm rom a tooth it produces an upright image that is 4.5 larger. a. What kind o mirror is used? Why? b. alculate the image distance and the ocal length o the mirror. Is the image is real or virtual and upright or inverted? Why? 3. Side view mirrors on cars oten state: Objects in mirror are closer than they appear. a. What kind o mirror is used? Why? b. When another car is 20.0 m away, the image seen in the mirror is one-third the size o the object. What is the radius o curvature or this mirror? 16

18 4. A mirror at an amusement park shows an upright image o any person who stands 1.4 m in ront o it. a. I the image is three times the person s height, what is the ocal length o this mirror? b. What type o mirror is used? Why? 5. A convex mirror with a radius o curvature o 45.0 cm orms a 1.70 cm tall image o a pencil at a distance o 15.8 cm behind the mirror. a. alculate the object distance and the object height or the pencil. b. alculate the magniication o the image. c. What is the image type and orientation? Why? 17