1 Physics 1403 Lenses It s party time, boys and girls, because today we wrap up our study of physics. We ll get this party started in a bit, but first, you have some more to learn about refracted light. So let s get started with this demo. Now, we ve told you over and over that light moves in straight lines unless it goes from one medium to another one with a different optical density. So why is it that I can shine laser light into one end of this curled acrylic rod, and it curls around and comes out the other end? Well, the phenomenon is called total internal reflection and it s the idea behind optical fibers and the reason diamonds sparkle. Watch this. Let s say that this is a pool of water, and an underwater light shines up from the bottom of the pool. When it reaches the surface, it goes from water to air, from a slow medium to a faster one. So how does the light refract or bend? Tell your teacher. It bends away from the normal, like this. So the angle of refraction, r is greater than the angle of incidence, i. Now let s increase the angle of incidence. What do you think will happen to the angle of refraction? As i increases, r also increases. As the angle of incidence continues to increase, so does the angle of refraction until eventually, we get an angle of refraction of 90 degrees, and the light skims across the surface of the water. The angle of incidence that produces an angle of refraction of 90 degrees is called the critical angle, i sub c. Now if we increase the angle of incidence even more, the angle of refraction is greater than 90 degrees. So instead of leaving the water, the light will reflect off the surface back down into the water. This is called total internal reflection. Total internal reflection occurs when i is greater than i c and no light leaves the medium. Now critical angles differ from one substance to another. A medium with a large index of refraction will have a small critical angle. For example, diamonds have an index of refraction of 2.42 and a critical angle of only 24 degrees. Light that enters one of the faces of a diamond is very likely to hit another face at an angle exceeding 24 degrees. So the light bounces around inside the diamond, eventually coming out of one of the faces. This explains why a diamond sparkles. Another interesting application of total internal reflection is the optical fiber. This light pipe is much larger than an optical fiber, but it works on the same principle. Watch this.
2 Optical fibers are made of a transparent substance with a very low critical angle. When light goes into the fiber at this end, it hits the wall here. And the angle of incidence is greater than the critical angle. So no light escapes out the side at this point. All of it is reflected internally to hit this side, and so on, and so on, so that most of the light that goes in comes out at this end. Of course, some of the light will hit the sides at an angle less than the critical angle, like this, and escape out the side. But even when the fiber is curved more, most of the light is transmitted. Optical fibers have many uses, from medicine to communications. Now let s move on to another practical application of refraction, the lens. You re probably familiar with magnifying lenses, contact lenses and glasses, and the lenses in optical devices such as binoculars. So let s look into lenses more closely and see how they affect light. We ll start with a triangle of glass, such as this prism, and go from there. (triangle on screen) You ve seen this before, but let s go over it one more time. When a light ray hits the glass at an angle, it goes from fast to slow and bends down, toward the normal. When it leaves the glass on this side, it goes from slow to fast and bends away from the normal, which also is down because this side has an opposite slant. Now, to make things really simple, we re going to average things out and show one light ray going straight into the middle of the triangle and then bending once toward the bottom of the triangle and coming out of the glass. Keep in mind that light bends toward the bottom of a triangle of glass. Your teacher will give you these diagrams of two sets of glass with a light ray going in. You draw the ray coming out of each piece of glass. Local Teachers, turn off the tape and give students problem set number one from the facilitator's guide. (Pause Tape Now graphic) Here s what you should have drawn for the first set of glass. Now, all we have to do is merge all the pieces and we have a convex lens. A convex lens is called a converging lens. Parallel light rays go through the lens and converge on the other side, at the focal point. Now here s what you should have drawn for the second set of glass pieces. And when you put the pieces together, you get a concave lens, which, as the name implies, caves in at the middle. A concave lens is called a diverging lens. Parallel light rays diverge as they leave the lens. They seem to come from behind the lens, at the virtual focal point, F prime. 2
3 (diagram of lens on screen) You ve already seen two parts that we ll need to draw ray diagrams, so let s finish labeling some other important parts. We ll use a convex lens for our drawing, but the parts are the same for a concave lens. First. let s label O, the optical center of the lens. And this is the principal axis, which goes through O. Our object will be on the left in this drawing, so light rays will move from the left, go through the lens, and come out on the right, where our eye is. If the object were a very large distance away, it would be like a small dot, and all the rays would come in parallel to each other. These rays will converge on the side of the lens where our eyes are, so this is called the real focus or the real focal point, F. The distance from the lens to F is the focal length, f. (picture on screen) To find the focal length of a lens, we let light from a distant object go through the lens and focus onto a screen. We then measure the distance from the image to the lens. And this same distance on the object side of the lens is F prime, which is called the virtual focus. To us, this point is behind the lens. For reference, we need two more points, twice the distance from the lens. We ll label these 2F on our eye side and 2F prime behind the lens. The object will always be placed on the prime side because light goes from it through the lens and to our eyes. Now we re ready to go into the lab to locate images formed by a convex lens. But first, you need one more physics challenge question. The focal length of a mirror depends only on the mirror s shape. But the focal length of a lens depends both on its shape and what other factor? Tell your teacher. The material that makes up the lens affects how much light rays bend. A lens made of a material with a high index of refraction will bend the light more than one with a low index of refraction. Now we re ready to go to the lab. Since we won t be doing any math with lens images, we won t give you any specific measurements in this lab. You ll use phrases like between F and 2F to describe locations. (Pause Tape Now graphic) (students on screen) Our students attach a convex lens to the middle of a meter stick. The focal length of the lens has already been determined, so the students label F, the focal point, and 2F. And since light rays will go from the object on one side of the lens to the other side, where our eyes are, we ll need reference points on the object side of the lens. Our students label F prime and 2F 3
4 prime. The object used in this lab will be a candle, and the flame will furnish the incident light rays going through the lens. For trial one, the candle is placed beyond 2F prime. Our students use a white paper screen to find the image. The image is found between F and 2F. Record this location 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 through the lens, you see the same image that was projected onto the screen. In fact, your eyes do not focus on the surface of the lens but on the image, between F and 2F. For trial two, our students move the candle to 2F prime. They find a real image at 2F. The image is real. It is the same size as the object and is inverted. Looking through the lens shows the same image that was projected onto the screen. For trial three, the candle is moved to a position between F prime and 2F prime. Our students locate the image on a screen held beyond 2F. The real image formed on the screen is enlarged and inverted. And when you look through the lens, you can that the image of the flame is enlarged and inverted. In trial four, the candle is moved closer to the lens, between F prime and the lens. Our students try to find a real image, but no image forms on the screen. When they look through the lens, a different image is seen. The image appears to be on the same side of the lens as the object. In fact, you can see the actual candle and the tip of the flame behind the lens. The image is virtual since it forms only in our minds. It is enlarged and erect. Did you notice a similarity between the convex lens and a concave mirror? They both form real and virtual images of all sizes, so they re versatile. The closer we bring the object to both, the farther away the image is and the larger it is. And when the object is placed very close to the concave mirror or convex lens, the image is erect, virtual, and enlarged. (boy with lens on screen) A convex lens projects real, inverted images of an object if the object is placed beyond the focal point. A magnified virtual image is projected if the object is placed between the focal point and the lens. Drawing ray diagrams to locate images produced by a convex lens is very similar to the procedure we used to locate mirror images. As before, we ll need some special rays that always behave the same. 4
5 This time, I m only going to show you two special rays to draw because they always work, no matter where the object is placed. Now remember that the object will be on one side of the lens and your eyes will be on the other side. So from your perspective, the object is behind the lens, on the virtual or prime side. The first incident ray is drawn from the object, our arrow tip, to the lens, parallel to the principal axis. Sound familiar? And how will this ray leave the lens? Tell your teacher. If you said through F, you re right. But which F? The answer is that rays going into a convex lens parallel to P will go out through F, not F prime. If you re not sure, imagine a triangle and remember that the ray always bends toward the base of the triangle. The next special ray is one that goes from the object to the lens, through O, the optical center. This ray hits the lens perpendicular to both surfaces, along the normal line. So it doesn t refract at all, but goes straight through the lens and out. How easy is that? Where the two rays meet, or seem to meet, you ll find the image. Drawing these ray diagrams should be easy for you, since you will draw the same two kinds of rays every time. So I want you to try six ray diagrams, starting with the object far from the lens, so that rays come in parallel to P, and ending with the object very close to the lens. In each case, describe the image and, with the exception of A and E, compare it to what you saw in the lab. Your teachers will give you the diagrams and time to complete the drawings. Then we ll go over the answers. Local Teachers, turn off the tape and give students problem set number two from the facilitator's guide. (Pause Tape Now graphic) Here are the images you should have drawn. In A, the object is far from the lens, so all the rays are coming in parallel to P. They converge at the focal point. In fact, this is how we found the focal length of the lens. The image is real, inverted, and reduced. B is the same as case one from the lab. The image is real, inverted, and reduced and is found between F and 2F. C is the same as case two from the lab. The image is real, inverted, and the same size as the object and is found at 2F. D is the same as case three from the lab. The image is real, inverted, and enlarged and is found beyond 2F. We didn t try E in the lab because it would be impossible to put the whole candle at F. Because the refracted rays are all parallel to each other, no image is found. F is the same as case four from the lab. The image is virtual, erect, and enlarged and appears to us behind the lens. 5
6 If you were stranded on a desert island, without any matches, you could start a fire using a convex lens. All you have to do is focus the sun s rays on something flammable. So where would you place the flammable materials? Tell your teacher. You d place the material at the focal point of the lens. Did you get it? Now why might you have a convex lens? I ll tell you later in this program. But first, let s go into the lab and investigate images formed by a concave lens. (students on screen) In this part of the lab, our students place a concave lens in a holder and attach it to a meter stick. They light a candle and place it in behind the lens. Then they try to find a real image by moving the screen back and forth in front of the lens, on the side opposite the object, but no image forms on the screen. Tell your teacher the type of image a concave lens must form. When our students look into the lens, here s what they see. All images formed by concave lenses appear to be behind the lens, so they are virtual. The images are reduced and erect. Let s look at a ray diagram to see why. The rules for drawing ray diagrams for concave lenses are almost the same as those for convex lenses. In fact, number two is identical. Rays from the object to the lens going through O will just keep on going straight. And the other special ray is pretty easy to figure out. This ray is coming into the lens parallel to P. And it s going to bend and come out of the lens through one of the focal points. You can remember that concave lenses are diverging lenses or you can just look for a triangle of glass, right here. And bend the ray toward the base of the triangle, which is upward. That means the ray goes through F prime. So turn the ruler like this and draw the outgoing ray. You can see that the rays diverge from the lens and won t meet on your eye side. So your mind takes over and extends the rays behind the lens. The image is erect, virtual, and reduced. You try this ray diagram. Your teacher will check your diagrams when you ve finished. Local Teachers, turn off the tape and give students problem set number three from the facilitator's guide. (Pause Tape Now graphic) So a concave lens acts very much like a convex mirror, producing a virtual, erect, and reduced image. And have you noticed that for lenses as well as for mirrors, virtual images are always erect, where real images are always inverted? We could do some math to confirm what your ray diagrams have shown you about the location and magnification of lens images. However, the lens equations are just like the mirror equations you used before, so we won t go into it in this program. But with all that extra time before final exams start, 6
7 you teacher might want to give you some problems. Instead of equations, let s talk about some uses for lenses. Of course, one important use is in eyeglasses and contact lenses. And you do know that the eye itself has a lens? Watch this. The lens in our eye is a convex lens. The focal length of the eye can be varied. Holding an object close to the eye makes it difficult to focus on objects across the room. Likewise, focusing on an object far away makes it difficult to focus on near objects. In order to focus the image of a close object on the eye s retina, the muscles of the eye contract in an attempt to make the lens more convex. As people age, the lenses become less elastic, causing difficulty in focusing on close objects. Reading glasses with convex lenses help individuals focus near objects on the retina. Near sighted people are unable to see distant objects clearly. Their eyes focus the images of far objects in front of the retina. This can be corrected by the use of concave lenses which cause the image to diverge slightly, landing on the retina. The images formed by the eye are inverted on the retina and then reversed by the brain. So if you re far sighted, the convex lenses in your reading glasses could be used to start a fire. But not all lenses are convex or concave. If you wear glasses, look at them from the side, and you ll see that one surface might be plane or flat and the other concave or convex. For this reason most physicists talk about converging or diverging lenses instead of about convex or concave shapes. Can you think of more uses for lenses? How about cameras, binoculars, telescopes, and microscopes? Some of these instruments use a combination of lenses. Put your pencils down, and we ll show you how a microscope forms its enlarged image. There are two lenses in a microscope, the objective close to the stage and the eyepiece. To make the ray diagrams easier to see, we re going to turn the microscope sideways, like this. Now, the object is on the stage, between F prime and 2F prime. The image is real, inverted, and enlarged. Now, the image from the first lens becomes the object for the second lens, located between F prime and the lens. Let s look at what happens with the eyepiece. The image formed by the eyepiece is virtual and enlarged again. And that s what we see. Look again at the object and the final image. Hard to believe but we are at the end of our year in physics At the beginning of the very first program, I told you that you were going to learn a lot this year, about the world around you and about your own skills and abilities. I hope you ve done just that and you ve had some fun along the way. I sure have most of the time. 7
8 no audio during clips Boy, these writers have thought of just about everything that could happen to me, short of a pie in the face. Thankfully, it s too late now. Good luck on your finals and good luck in college. All right. Let s get this wrap-up party started... Oh nooooo! I was just kidding about the pie in the face! 8