PHY 104 Lab 12: Introduction to Optics

Transcription

1 PHY 104 Lab 12: Introduction to Optics , James J. DeHaven, Ph.D. Optics is the study of light and the instruments we use (such as lenses, prisms and mirrors) to control and measure it. In today s lab, we will examine the following areas of optics: 1) Color 2) Refraction 3) Reflection 4) Mirrors 5) Thin Convex Lens: the lens equation 6) Corrective lenses 7) The telescope Most of the experiments will require you to make qualitative observations and comment on them and explain them in your lab report. One experiment (the lens equation) will require numerical analysis. Note: Make sure to print out the last page of this lab and bring it with you. Introduction -1 - The basic optical components used in everyday life include prisms mirrors and lenses. Prisms are employed to reflect light (by means of a process called total internal reflection), to alter the direction of light via refraction, and to break white light up into its component colors. We will examine the effect of a prism on light for the latter two cases, and we will also examine the recombination of colored light into white light. There are two varieties of simple lenses: concave and convex. Figures 1 and 2 illustrate how these lenses interact with parallel rays of light. Parallel rays of light typify the light coming from a distant source. Though light is reflected from an object in all directions, a lens far away from an object intercepts rays that are nearly parallel. In the case of a convex lens, these rays come to a focus on the side of the lens opposite the source of the light. The distance from the center of the lens to where these rays of light cross is known as the focal length of the lens. Figure 1: Convex Lens

2 -2 - Figure 2: Concave Lens Light from a convex lens, on the other hand, diverges. To an observer, the rays of light seem to emanate from a point source on the same side of the lens as the source of light. This point is also called the focal point of the lens. For a concave lens the focal point is considered to be a negative number. In general the focal length is positive for converging (convex) lenses, and negative for diverging (concave) lenses. Concave mirrors influence light in a manner similar to convex lenses (figure 3). Again, the rays of parallel light converge at a single point, the focal point of the mirror. You may recall observing a similar behavior for a Figure 3: Concave Mirror

3 Figure 3: Concave Mirror -3 - water-wave reflector in the ripple tank experiment. For a spherical mirror, the focal length is equal to precisely 1/2 of the radius of curvature of the mirror (We imagine the mirror to be a section of an imaginary sphere to visualize this.) This relationship is shown in figure 4. f C Figure 4: Focal length for a Concave Mirror Convex mirrors cause parallel rays of light to diverge. The focal length is also equal to half the radius of curvature, but is located on the side of the mirror opposite to the incident light. The focal length of a convex mirror, like that of a concave lens, is considered by convention to be negative. Figure 5: Convex Mirror

4 Figure 5: Convex Mirror -4 - The focal length of a thin convex lens can be determined using the so-called lens equation. Consider the experimental setup shown in figure 6. An object is located some distance from a lens, do, known as the object distance. If do is greater than the focal length, f, of the lens, an image will be formed on the opposite side of the lens at some distance, di, away from the lens, also called the image distance. d o f focal point object d i image Figure 6: Determination of the focal length of a thin convex lens using the lens equation The geometry of this setup is determined by the so-called lens equation: [1] 1 f = 1 + d i d o 1 As you might deduce from the drawing, the image may be magnified or demagnified. The extent of this magnification is determined by the relative magnitudes of the image and object distances according to the following: [2] M = d i d o The negative sign implies that the image is inverted. It is possible to make an upright image by using a combination of lenses or by using a lens whose image distance is opposite in sign to its object distance. The sign conventions for utilizing these equations are as follows: 1) The focal length (as noted above) is positive for converging lenses and negative for diverging lenses. 2) The object distance is positive if the object is on the same side of the lens as that from which the light is coming. Usually the object distance is negative only in situations in which several lenses are used together. 3) The image distance is positive if it is on the opposite side of the lens from that from which the light is

5 coming. When the image distance is positive, we have a real image; when it is negative we have a virtual image. 4) Object and image heights are positive for points above the axis and negative for points below it. Thin convex lenses can be used in combination with each other to perform a variety of tasks involving magnification. When the object is far away, we use an arrangement of lenses known as a telescope. When the object is close, we use an arrangement known as a microscope Childhood Adolescence Convex and concave lenses can also be used to assist humans in vision. In a person with normal vision (figure 7), the eye s lens can focus light on the retina, and form an image of what exists in the outside world. Note that the magnification is less than one--the image is demagnified and is also inverted. Such vision is common, though not universal, among young children. As the eye grows, the distance from the lens to the retina can become so large that the lens can no longer bring the image to a focus on the retina; rather it brings it to a focus at some distance in front of the retina. This growth frequently accompanies the adolescent growth spurt, and many people first become aware of the need for corrective lenses at that time. Eyeglasses can correct this condition (known as myopia) as follows: the excessive convergence of the eye s lens is compensated by placing a diverging lens in front of it. The progression from normal vision, through myopia, to vision corrected by eyeglasses, is shown in figure 7. Corrective Lenses Figure 7: Normal vision, myopia (onset frequently during adolescence), and the restoration of normal vision via corrective lenses contrasted

6 -6 - Experimental In many of the procedures in this lab, you will need a source of light. There are two kinds that we use, both of which perform the same functions: they produce from 1 to 5 pencil thin rays of light, they produce bars of red, green and blue light, they act as a point source of light, and they provide a lighted object for our investigations of the lens equation, corrective lenses, and the telescope. One variety, the newer of the two, is to be used with the mechanics tacks (which have been adapted to be used as optical bench), and the other older variety is to be used in conjunction with the conventional older optical bench apparatus. See figure 8 for photographs of these items. Figure 8: Light sources, old and new Colors Place the light source on a large white piece of paper and place the converging lens (from the ray optics kit) in front of it. Adjust the source so that three parallel stripes of light, red, green, and blue, skim across the paper and are visible. Figure 9: Mixing three colors with a converging lens

7 What is the color of the light at the intersection region of the three rays? Block each ray separately with a pencil, so that only two colors at a time are combining. What are these colors. Compare your results with the color generator on the Macintosh computer. To access this choose SYSTEM PREFERENCES under the APPLE menu. In the window that opens up, click on APPEARANCE. (It should be the first icon.) Look for the HIGHLIGHT COLOR pop-up menu and choose OTHER... Click on the SLIDERS icon and choose RGB SLIDERS from the pop-up menu. Mix together 100% of all three colors, then mix in 100% of two colors, and zero percent of the third. See if this matches your observation with the lens and color stripes. Red green and blue are sometimes referred to as primary colors, because all other colors can be generated by mixing these three in the proper proportion. Color separation -7 - White light can be broken into its component colors by means of a prism. Configure a prism as shown in Figure 10 with a single ray of white light from the light source. Again, make your observations by allowing the light to skim along the table top. White Light Color Spectrum Figure 10: Orienting the prism for production of a color spectrum from white light Refraction Observe the change in direction of a single ray of light using the prism as shown in Figure 11: Where does the refracted light emerge? Figure 11: Orienting the prism for observing refraction. This is an overhead view. What is the path traveled by the ray as it passes through the prism?

8 -8 - Reflection Using a single ray and the plane mirror from the plane mirror from the ray optics kit, verify that the angle of incidence equals the angle of reflection. To do this, draw a line along the prism surface and then two other lines representing the incident and reflected rays. Using five rays from the light box, study the convex and concave mirrors, and verify that their behavior is similar to that depicted in figure 3 and 5. Refraction Again using five rays and a piece of white paper, trace the rays for a concave and convex lens (from the ray optics box) and verify that these resemble the behavior shown in figure 1 and 2. Use the convex and concave lens in combination with each other to observe the effect of corrective lenses. To do this place the convex lens 12 cm from the light source (which should be set for 5 parallel rays). Note the location of the focal point, and then insert the corrective lens (the concave lens) directly in front of the light source. Note how the position of the focal point changes. Lens Equation The remainder of this experiment will be performed using the optical bench. As noted above, we use two slightly different optical bench systems, one a specialized piece of equipment and the other newer system based on the mechanics tracks that we have used throughout the year. Figure 12 shows a comparison shot of the two setups. Figure 12: Comparing the old and new optical bench apparatus

9 -9 - In figure 12, each bench is configured with a light source, a lens and viewing screen. The typical lens (Figure 13) is mounted in a small plastic holder which snaps into a groove on the older optics track. The lens will not mount properly on the mechanics tracks, however, unless it is provided with the appropriate adapter. This adapter is shown in Figure 14, along with a photo of an adapter with a properly mounted lens holder. Figure 13: Standard lens and lens holder Figure 14: Mechanics track adapter (left) and adapter with a standard lens holder mounted in it

10 -10 - The mechanics track also permits the use of off-the-shelf lenses by means of a circular mounting bracket, which also mounts in a mechanics track optics adapter. To use this you must know the diameter of your lens (ours are mostly 50 mm, and then set the two bottom mounting posts to the diameter of lens. (You have to loosen their set screws to move them.) You then insert the lens and move the top mounting post into place. This procedure is illustrated in the left hand panel of Figure 15, and in the right hand panel, we see a completely assembled lens mount. Figure 15: Adjusting the lens mount post for a 50 mm lens (left) and the assembled lens mount (right) Mount the light source in the light source bracket and secure this to the optical bench so that the targetshaped object points down the optical bench. On the old bench the object should be mounted at the 10 cm mark, and the viewing screen at the 110 cm mark and turn on the light source. If you are using the optical bench, the leveling feet should be at 40 and 170 cm, and the light source should be at the 50 cm mark and the viewing screen at the 150 cm mark. Note that we are simply beginning with a 100 cm distance between source and screen regardless of which apparatus we are using. Now place the 100 mm lens between the object (the light source) and the screen. Although the lens is nominally a 10 cm focal length lens, its precise focal length may be somewhat different. There will be two positions at which the lens will form a clear, focused image on the viewing screen. In one case the image will be smaller than the object (the target-shaped light source). In the other case the image will be bigger. Enter your results into a facsimile of Table 1 in your notebook. Calculate the focal lengths for the two positions of the length. These should be close to each other. They may be the same. Measure the image size. The object is calibrated in mm, but its image, if it is magnified may be of a different size. The inner circle on the object has a radius of 5 mm. What is the radius of this circle at the image? Is it magnified? Use equation [1] and [2] to calculate the focal length and the magnification.

11 -11 - Location of d i d o Large Image Screen ƒ ƒ Size d i d o Small Image Size 110/150 90/130 70/110 50/90 Repeat this experiment for screen locations of 90, 70, and 50 cm (130, 110, and 90, if you are using the mechanics track). Be careful to measure the distance from the object to the lens and the distance from the image to the lens for d o, and d i, respectively. Note that it will probably be impossible to measure the smaller image for the first two locations--it is just plain too small. At the end of this experiment, you will have obtained 8 separate values for the focal length of the lens--they should all be close to each other. Find their average and their standard deviation. Using the average value you have obtained, place the lens precisely 2ƒ (2 focal lengths) away from the object. Move the screen to where you get a focused image. Where is the prediction of equations 1 and 2 for the image distance and magnification? Is this confirmed by your data? Eyeglasses Table 1: Data Table for lens equation experiment (Location of Screen = conventional optical bench/mechanics track) In this experiment you will use a converging lens to mimic the eye s lens, the viewing screen to emulate the retina, and a diverging lens to illustrate the effect of corrective eye wear. Work with the light source/target object, located at the 10 cm mark on the optical bench (mechanics track should be 50 cm). Place the screen (the retina) at the 80 cm mark (120 cm on the mechanics track). Place the 100 mm lens and move it until the image is focused on the viewing screen. Choose the position where the lens is far from the object and the image is reduced in size (this is exactly the arrangement in your own eye). Now allow the eye to grow. Without moving the convex lens, move the viewing back to the 85 cm mark (125 cm mark on the mechanics track). The image will now go out of focus and resembles what happens when your eye grows more than it is possible for the lens to accommodate. Correct your vision by inserting eyeglasses. In other words, place the 150mm lens between the convex

12 -12 - lens and the light source, and then move it until the image comes into focus on the viewing screen. Telescope One common optical instrument is the terrestrial telescope. We will construct a crude telescope using two convex lenses, a 250 mm focal length objective and a 100 mm eyepiece. In a telescope, the objective lens forms an image of a distant object, and the eyepiece magnifies this image. The magnification is given by the ratio of the focal length of the objective to that of the eyepiece. OBJECT 250 mm objective Telescope 100 mm eyepiece Figure 16: Schematic diagram of an optical bench telescope In this experiment, your object will be the viewing screen, to which you have attached the piece of grid paper located in the lab report. Place the object at the 10 cm mark on the optical bench (50 cm mark on the mechanics track, and the eyepiece at the 110 cm mark (150 cm mark on the mechanics track). Place the objective lens between the eyepiece and the object. View with your eye as close as possible to the eyepiece, and move the objective until you can see the grid clearly in focus in the eyepiece. Open both eyes, looking through the eyepiece with one, and at the paper unaided with the other. This will give you an idea of how effectively the telescope magnifies objects.

13 -13 - Report: Introduction: Write a brief introduction stating the objectives of the experiment, and a concise summary of the methods that will be used. Experimental: Describe the experimental apparatus and precisely what variables will be measured and how they will be measured. Results: Summarize the results of the experiment. Show sample calculations. If you are attaching computer generated tables or graphs, briefly explain them here. Discussion: Explain the significance of your results and their connection with more general physical principles. Where it is possible, compare your numbers with accepted values. Explain any sources of error.

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