1 Physics 1401 Mirrors You ve probably heard the old saying, The end is in sight. Well, that saying applies doubly to our class. Not only do we start the final unit that ends our year of physics but today we are actually going to deal with sight. Our subject is optics, namely the study of mirrors, lenses, and other topics related to sight. To get things started, I m going to show you something that I ll want you to explain later. For now, just watch and be impressed. I have two beakers, and I ll put the smaller one inside the larger one. As you would expect, you can see both beakers. Now I ll fill the smaller beaker with corn oil. And you can still see both beakers. But watch what happens as the smaller beaker overflows. It disappears. You can see the markings on it, but that s all. So why can t you see the small beaker? During this class you ll be getting clues that will help you solve the mystery of the disappearing beaker. Save a page in your notes, and watch for this sign. After you ve collected all the clues, your teacher will ask you to explain why the beaker disappears. (clue #1 on screen) Here s your first clue. We know that the only way to see a non-luminous object is for light to strike it and reflect back to our eyes. In our study of waves, you learned how a wave behaves when it hits the boundary of a new medium. Sometimes it reflects back, sometimes it goes straight through to the new medium, and sometimes it bends. Go back to your unit 11 notes on waves to find out what determines how much light wave energy is reflected and how much is transmitted. We ll start our study of optics with reflection. Now you know that light waves travel in straight lines until they hit a boundary of some sort. When light from this studio goes from my face to this mirror, I can see my reflection, or my reflected image. Now here is a piece of white paper. You learned in our last program that white objects reflect light. So why can t I see my image when I look at this white board? Well, when light reflects off of a surface, it obeys the Law of Reflection. Tell your teacher what this law states. Did you say that the angle of incidence equals the angle of reflection? That s right. Now, even though this white board looks smooth, it s not. So when parallel rays of light strike it, each one is reflected in a different direction, obeying the Law of Reflection. This is called diffuse reflection. (text on screen) In diffuse reflection, parallel incident light rays are reflected in different directions. But when parallel rays of light strike a very smooth surface such as this mirror, all the reflected rays are parallel, too. This is called regular reflection. () In regular reflection, parallel incident light rays are reflected parallel. Mirrors are examples of regular reflection. Today, we ll be studying mirrors, which are made of polished glass, usually coated on the back with silver or another metal. But let s start with a piece of uncoated glass, which can also act like a mirror.
2 I can see my reflection in this one. (candle and beaker on screen) Our student stands behind a lit candle, looking into the glass plate toward the beaker of water behind it. In addition to the actual candle, he sees an image of the candle, which appears to be burning inside the water. When we look at the beaker from the side, no image appears. We must look through the plate to see the image. Even though a glass plate isn t a very good mirror, it does have an advantage. We can actually look through the glass plate to see the beaker of water behind it. But how did the image of the burning candle get back there, too? We all know that the candle is not really there. And if we didn t look through the glass plate, we wouldn t see the image in the beaker at all. If an actual mirror were used, we wouldn t be able to see through it, but we d still see the image of the candle in the mirror. How can this be? The answer is that the image is a virtual image, one that is formed in our minds. You know that virtual reality is in our minds. And when your mom says that you are virtually a genius, she means that you are a genius in her mind, not a real one. So, even for us non-genius types, it s easy to remember that virtual images are in the mind. Let s use the Law of Reflection to see how flat mirrors, also called plane mirrors, form virtual images. Put your pencils down and watch for now. You ll take notes on all this later. We re going to draw a ray diagram to find the image of our object, which in this case is a candle. The object is the source of the light rays, either because it is luminous, like the candle flame, or because it is illuminated by light in the room. So light rays will go from the object to the mirror and then be reflected back toward our eyes. Now, we re going to use these two incident light rays to locate the image of the very tip of the flame. The image will form where the two reflected rays converge or intersect. Let s start with the one that hits the mirror straight on. At the point of incidence, the ray will be reflected. And the angle of reflection will be equal to the angle of incidence, which is 0 o. So I ll use a solid line to draw the reflected ray straight back along the same line. All we need is one more reflected ray to locate an image. Here s our second incident ray. To save time, I ve already used a protractor to measure the angle of incidence and I ve drawn the reflected ray at the same angle. Now, look at the two reflected rays. Will these rays ever intersect in front of the mirror? No, but our minds take over at this point, and we extend the rays in straight lines to the point where they seem to meet. Let s do that. This is the image point, the point where the rays seem to meet. Notice that the image seems to be behind the mirror, the same distance that the object is in front of the mirror. And if we used the same method to find the image of this point at the base of the candle, and of all 2
3 points in between, we d get this as the image of the entire candle. Notice that it s the same distance behind the mirror as the object is in front of it, and it s the same size as the object. It s time for some notes. (green chalkboard on screen) Since our minds must help to form plane mirror images, they are called virtual images. Virtual images are formed by reflected light rays that appear to converge but never really do converge. Plane mirror images appear to form behind the mirror, the same distance from the mirror as the object is in front of it. Plane mirror images are the same size as the object. They are erect. Left and right seem to be reversed in plane mirrors. Let s talk about a couple of uses for plane mirrors, other than the obvious ones. Have you ever had your eyes tested with the big eye chart on a wall? Well, to test your vision at a distance, you d have to put the chart at the end of a long hall. But many optometrist offices are equipped with plane mirrors placed on the wall in front of you. The eye chart is projected on the wall behind you, so that you focus on the image in the mirror, which is as far behind the mirror as the chart is in front of it. Of course, since plane mirrors reverse left and right, the chart must be printed with the letters backward so you can read it. Another use for plane mirrors is the rear-view mirror in a car. You already knew that, but did you know why the mirror is tilted at night to prevent glare from the headlights behind you? Well, mirrors consist of a piece of glass that is silvered on the back, like this. When you tip the mirror upward, you re changing the angles of incidence and reflection so that the reflected light from the headlights goes over your head. It s the light reflecting off the surface of the glass in front of the mirror that hits your eyes. And glass by itself doesn t reflect a lot of light. It s that simple. OK, it s time to look at another type of mirror. Mirrors can be curved as well as flat. Mirrors that are curved inward are called concave, and mirrors that curve outward are convex mirrors. Curved mirrors are sometimes called spherical mirrors. There are two types, depending on which side is used as the reflecting surface. And the images they form are very different from plane mirror images. If the mirror reflects light from its inner, or caved in surface, like the inside of this spoon, it s called a concave mirror. 3
4 And if it reflects light from its outer surface, like the back of the spoon, it s called a convex mirror. You ll want to grab a ruler or some other straight edge now. When you ve done so, you ll get some notes on the parts of a spherical mirror and learn how to draw ray diagrams to locate images. I ll be showing you the parts of a concave mirror, but the parts of a convex mirror will be the same. The only difference is that this part of the mirror would be the reflecting side of a convex mirror. As you can see, spherical mirrors are part of a sphere. And the first point I want you to label is C, the center of curvature. This is the geometric center of the sphere. And label this point V, the vertex of the mirror. This is the center of the mirror itself. Next, label this point capitol F, the focal point of the mirror. This is the point where parallel rays of light will meet. Label this line P. It goes through both C and F and is called the principal axis. Now, the distance between C and V is labeled r. This is the radius of curvature. And finally, the distance between F and V is called the focal length of the mirror, labeled lower case f. For small mirrors, like the ones we ll use in the lab, r equals two times f. Concave mirrors are called converging mirrors because parallel rays of light, like those coming from a distant object, will converge at the focal point and form a real image. (green chalkboard on screen) A real image is formed when reflected rays actually converge at a point. A real image can be projected on a screen. You ll fill in one more fact about real images after the lab, so save room. The best way to find the focal point of a concave mirror is to focus light from a distant object onto the mirror. When you look into a concave mirror and focus on a distant object, your eyes are really focusing on the focal point, not on the surface of the mirror. And you can hold a screen at that point and get a real image on the screen. (picture on screen) This shows a concave mirror pointed at a tree. The cardboard screen is held at the focal point, and an inverted image of the tree can be seen on the screen. When the screen is held a few centimeters away from the focal point, you can see that the image is not clear. In a minute, we re going into the lab to watch our students find images of a candle flame placed at different positions in front of the mirror. They will use the paper screen to locate real images. Your teacher will pause the tape now and give you the lab sheet. When you come back, we ll go straight to the lab. 4
5 (Pause Tape Now graphic) (students on screen) Our students attach a concave mirror to a meter stick, at the 10 centimeter position. The focal length of the mirror has already been determined to be 20 centimeters. The students label F, the focal point, at the 30 centimeter mark, 20 centimeter from the mirror. Then they label C, the center of curvature, 40 centimeters from the mirror, at the 50 centimeter position on the meter stick. The object used in this lab will be a candle, since the flame will furnish the incident light rays going to the mirror. For trial one, the candle is placed beyond C, at the 70 centimeter mark. This makes the distance of the object, d o 60 centimeters. Our students use a white paper screen to find the image. The image is found between C and F, 30 centimeters from the mirror. Record this distance as d i, and write between C and F in your data table. Because the image forms on the screen, it is a real image. And you can see that the image is reduced and inverted. Record your observations in the data table for trial one. When you look into the mirror, you see the same image that was projected onto the screen. In fact, your eyes do not focus on the surface of the mirror, but on the image, 30 centimeters from the mirror. For trial two, our students move the candle to C, 40 centimeters from the mirror. They find a real image at C. The image is real. It is the same size as the object and is inverted. Looking into the mirror shows the same image that was projected onto the screen. For trial three, the candle is moved to a position between C and F, 28 centimeters from the mirror. Our students locate the image on a screen held 70 centimeters from the mirror. The real image is enlarged and inverted. And the image seen in the mirror is the same. For trial four, the candle is moved even closer, between F and the mirror. D o for this trial is 10 centimeters. Our students try to find a real image, but no image forms on the screen. When they look into the mirror, a different image is seen. The image appears to be behind the mirror. It is virtual, since it forms only in our minds. It is enlarged and erect. 5
6 Hang on to your lab sheet. We ll use it later to compare what your observations to the images you draw using ray diagrams. Now, about those ray diagrams It would be very difficult to apply the Law of Reflection to spherical mirrors. So we rely on three special rays because they always reflect in the same way. We ll show you one at a time. The first special ray we use in every ray diagram is an incident ray parallel to the principal axis. It is reflected through F. If this object were far, far away from our mirror, it would be like a single point, and all the rays from it would cross the focal point. But objects close to the mirror have light coming from it to the mirror in all directions. The only ray that reflects through F is one that comes in parallel to P. The next ray that we often use is an incident ray that goes through F and then hits the mirror. Tell your teacher how you think this ray is reflected. Rays coming in through F are reflected parallel to P, just the opposite of ray number one. The third ray we use is the easiest. Incident rays that go from the object to the mirror and pass through C hit the mirror straight on. That s because the ray is coming in along the radius of the circle. So these rays are reflected straight back along the same line. OK. We have three rays that we can use to find an image, but all we need is two. You ll see that in some situations, rays one and two will work, and in other situations, rays one and three will work. So you need to know all three. It s best to use a straight edge and a sharp pencil. And to keep you from getting confused, let s agree to draw incident rays as dotted lines, and reflected rays as solid lines. The image forms where the solid reflected rays cross. We ll draw one together and then let you try some on your own. In all our ray diagrams, you ll be asked to draw the image of an arrow that is sitting on the principal axis. All you have to do is find the image point of the tip of the arrow. The rest of the arrow will line up with the tip, and the base of the image will rest on the principal axis. I ll show you what I mean in a minute. Now we ll always draw the first ray from the arrow tip parallel to the P. Use a dotted line for incident rays. When it hits the mirror, it will reflect through F, like this. We ll use a solid line, with an arrow to show the reflected ray. Next, we ll draw a ray in through F, with a dotted line. And how will this ray be reflected? Out parallel to P, like this. Now, we ve found the image point and can stop and draw the image of the arrow. The tip of the image will be at this point, where two reflected rays cross. To complete the image, we just connect the tip to the principal axis, like this. In this situation, the third ray will work, too. We don t need this one now, but let me show you that it works. We ll go from the object in to the mirror through C. And the reflected ray will be back along 6
7 the same line. You can see that all three reflected rays cross at the same point. Now, let s look at the image. Now fill in the facts about the image in your notes. The image is located between C and F. It s real because the reflected rays actually converge. And it is inverted, as all real images are. Finally, it is reduced. Look at your lab results for trial one, in which the candle was placed beyond C. The image you drew should have the same properties as the one you observed in the lab. So the diagrams really work. Let s try one more together, and then you ll draw some ray diagrams on your own. No matter where the object is, we ll always use ray number one, in parallel to P and out through F. Now, if you try to use ray number two, you ll see that a ray through F and our object doesn t hit on the mirror. That s why we need number three. We go from the object to the mirror, through C. So line up your ruler with C and the arrow tip. It doesn t matter what the order is. When the ray hits the mirror, it reflects straight back along the same line, so draw a solid reflected ray. You can see that the reflected rays diverge. They will never cross in front of the mirror. So our minds extend the rays behind the mirror to form a virtual image. All we have to do is complete the image of the entire object. Now fill in the facts about the image. When you put your face close to a large concave mirror, your image will be enlarged and erect. It s called a magnifying mirror when it s used like this. Now I have three more ray diagrams I want you to draw. Your teacher will give them to you. Come back when you ve found and described the images. Local Teachers, turn off the tape and give students problem set number one from the facilitator's guide. (Pause Tape Now graphic) In the first diagram, we use a ray in parallel to P and out through F, and then a ray in through F and out parallel to P. The image forms at C. It is a real image. Of course, it s inverted, and this time the image is the same size as the object. You saw this in the lab in trial two. In the second problem, we bring the object in closer to the mirror, between C and F. We go in parallel to P and out through F, and then you could draw a ray in through F and out parallel to P or in and out through C. Either way, the image produced is beyond C, real, inverted, and enlarged. You saw this in the lab as trial three. The last diagram is one that you didn t see in the lab because it would be impossible to put the threedimensional candle exactly at F. To draw the diagram, we go in parallel to P and out through F and then in and out through C. The reflected rays are parallel to each other. They will never meet in front or behind the mirror. So no image will form. 7
8 You might think that there wouldn t be a good use for placing an object at the focal point of a mirror, since no image forms. Well, look at this flashlight. This is a concave mirror, and the bulb is placed at the focal point. Light rays from the bulb hit the mirror and are reflected parallel to each other, forming a larger beam. Car headlights operate on the same principal. Now look at this clip to see some more uses for concave mirrors. (mirror on screen) Concave mirrors are used in a variety of applications. Make-up mirrors used to magnify the face are concave. Concave mirrors shaped as a parabola are placed behind the bulb of flashlights and headlights. These parabolic mirrors focus light waves into powerful beams. At this national laboratory, parabolic mirros are used to focus the sun s rays on heat motors that drive electric generators. These concave mirrors at a solar power plant in the Mohave desert focus light energy on tubes of heat absorbing oil. That s it for today s program. Your teacher has the Show What You Know questions for you. But before you leave, check this out. Look closely at this little pink pig. When I try to pick it up, my fingers go right through it. What s up with that? See if you can figure it out. I ll show you the trick at the beginning of our next program. And don t forget about the disappearing beaker. We ll see if you can find it next time. See you later. 8