PHYS 1020 LAB 7: LENSES AND OPTICS Note: Print and complete the separate pre-lab assignment BEFORE the lab. Hand it in at the start of the lab. Pre-Lab Start by reading the entire prelab and lab write-up. When a light ray strikes a smooth surface separating two transparent materials (like air, glass, or water), the wave is both partially reflected from the surface and partly refracted (or transmitted) into the second material. Start by downloading and opening the PhET sim you will be using: http://www.colorado.edu/physics/phet/dev/light-reflection-and-refraction/0.00.21/lightreflection-and-refraction_en.jnlp Analysis: 1) What do you notice about the angle of the reflected light in comparison with the angle of the incident light? (Note that there is a protractor on the PhET sim that you can use to measure angles!) 2) Now let s look at the refracted light. In general, the relationship between the angles of refracted light and a property of the media is given by: n 1 sin( 1 ) = n 2 sin( 2 ) or Here corresponds to the angle in the top medium and to the angle in the bottom medium. Both of these angles are measured from the z-axis down to the light (or up to the light in the media below). Similarly, n 1 and n 2 are the indices of refraction of the top and bottom material, respectively. (These numbers are shown on the PhET sim.) Now find a way to verify the relation given above on the PhET sim. You will want to take at least three data points at either different angles or different indices of refraction (you get to choose which!) or you may want to do both. Show all of your work in doing this and give a brief (2-3 sentences) description of the method you used to complete this problem. Additional Questions: 1. What is the definition of the focal length of a lens of curved mirror? 2. What does is mean for an image to be real? For an image to be virtual?
Lab 7: Lenses and Optics Lab Logistics: (continuous reminder) You and your group will work together to complete the lab. Remember, everyone will need to assume a different role from last week. For instance, if you were the manager last week, then you should either be the recorder or the skeptic for this lab. Again, everyone should be helping with the hands-on stuff. Again if you are part of a group of two, you should be switching each week who is the manager and who is the recorder. NO ONE SHOULD BE RECORDER TWO LABS IN A ROW. The manager: This person is responsible for making sure that the group follows the lab procedure and completes everything that is asked for in the lab. The collector recorder: This person is responsible for keeping the lab notebook for the day, recording the observations observed by the group and the group s answers to the questions asked in the lab. The skeptic: This person is there to question the results of the lab. Is everything making sense? Are we taking the data correctly? Are the results and conclusions reasonable? Did we skip a step? Begin each lab report by titling the lab, listing your lab partners who are present, and listing the jobs that each lab partner has assumed for the lab. Remember, your lab report should give an explanation of all of your observations and measurements. Also, you need to think of and try one additional experiment for either Part 1, 2, or 3 of this lab that will further test your explanation of the results that you found. (If time permits) Lab Description: Lenses are the basis for many modern optical instruments, such as microscopes, telescopes, cameras and eyeglasses. In this experiment you will work with two lenses. You will measure their focal lengths in several ways and study the magnification (how much the image of the object is smaller or larger than the object itself). Finally, you will use both of them to measure the chromatic aberrations (differences between how the lens bends red light and how it bends blue light) of one of the lenses. The main properties of any thin lens are summarized by the thin lens equation: (1) In this equation, f is the focal length of the lens and is positive for converging lenses (which you will be using in this experiment) and negative for diverging lenses. As shown in Fig. 1, d o is the distance from the object to the lens, and is positive for real objects (which is all that will be considered for this lab). Similarly, d i is the distance from the image to the lens and is positive for real images (as in Fig. 1) but negative for virtual images. (For example, a single diverging lens will always produce a virtual image from a real object, why?)
d o h o Image Object F F h i d i Fig. 1. The distances d o and d i that appear in the lens equation, illustrated for the case of a real image produced by a converging lens. The two points labeled F are the focal points of the lens. Part I: Focal lengths and Magnification factors The first part of this lab is to find the focal length of lens A by measuring values d i and d o and using eq. (1) to calculate the focal length. 1) Use the lighted object and lens A to create an image of the object (in focus) on the frosted glass screen. Is the image larger, smaller or the same size as the object? 2) For lens A, make three sets of measurements of d o, d i, h i and h o. h o is the height of the object and h i is the height of the image. Between each set adjust the distance between the object and the lens. Make sure you have at least one measurement where the image is smaller than the object and one where it is bigger than the object. Using the lens equation above, find the focal length, f, for lens A in each case. Estimate your uncertainty and discuss how you got it. 3) In Fig. 1, the image is smaller than the object. Using Fig. 1 as a model, draw a similar sketch which shows the object location and light rays that would form an image larger than the object. Your drawing should show the lens, the focal point of the lens, the object location, the rays coming off one point on the object and where the image will be formed by those rays. Note in Fig. 1 the light rays shown are coming from the object passing through the lens and where they cross they will form the image in focus. The three rays drawn are special since we know how they will bend using the following guidelines: a. When light rays come in parallel to the axis of the lens, they are bent by the lens such that they pass through the focal point.
b. Rays that pass through the focal point of the lens before hitting the lens are bent by the lens such that they exit parallel to the axis of the lens. c. Rays that pass through the very center of the lens exit the lens going in the same direction they were going originally. 4) As you bring the object closer and closer to the lens does the image get smaller or larger? At what distance will the lens no longer create an image in focus? Why? Make sure you make a prediction before you try it. 5) With the image in focus on the frosted glass screen, where do you think the image will be located if you place the object at the current location of the screen? Explain your thinking. Test it. 6) Use your measurements of the sizes, h i and h o, of the image and object to compute the magnification of the object for one of the measurements you made: Referring to Fig. 1 and using the fact that with similar triangles (all the angles are the same) the ratio of the sides are also the same (e.g., d i /h i =d o /d i ), you can see that M is also equal to Check the agreement between the two expressions for M by using your measurements. (So, if you know the image and object distances, you know the magnification!) Did you verify this? Part II: Alternative Method to determine focal length The second part of this experiment is to measure the focal length for both lenses. 1) How can you arrange a lens and a point source so that the rays that are coming out are parallel to one another? Use lens A and the point source (remove the arrow cover) so that the rays are coming out of the lens are all parallel as in Fig. 2. Recreate Fig. 2 being careful to identify where the 2 focal points are. point source Lens diameter beam diameter (D) f
Fig. 2. When a converging lens produces a parallel beam of light we say the light is collimated. This happens when the source is at the lens s focal point (d o = f). You can check that the light is collimated by seeing if the diameter, D, of the beam at points far from the lens is equal to the diameter of the lens itself. 2) Measure the distance from the point source to the lens. Is it equal to f A, the focal length of lens A, you measured in part I? Does it match your prediction for how you would need to arrange the point source and lens so that all the exiting rays were parallel? 3) Now place lens B in the collimated beam produced by lens A as in Fig. 3. Since the light rays approach B travelling parallel, the object distance for B is infinite and the image distance should be the focal length of B. What is the focal length for lens B? A Collimated beam B Dist to image = focal len. of B Fig. 3. Using a collimated beam to measure f B Part III: Chromatic Aberrations (Color matters) Still using the point source of light, you can study the chromatic aberration of lenses A and B. Chromatic aberration (slight differences in the lens s focusing properties for different colors or frequencies of light) occurs in all but the most expensive lenses (which are not made from a single material and are actually more than one lens combined into one). 1) Set your lenses up as shown in Fig. 3. Use a white piece of paper to closely examine the light beam as it focuses to a point. Locate the focus point and then move the piece of paper back and forth so that you can see the rays converging to the point and then diverging again once they pass through the point. What do you notice about the color/hue of the outer most ring of the light circle? Is it the same when the rays ar converging and diverging? Record your observations. 2) What do your observations tell you about how much the lenses are bending red light vs. how much they are bending blue light? Use a drawing to back up your claim. Recall that the amount of bending depends on the difference in the speed of light between the air and the glass. Both red light and blue light travel more slowly in glass than in air, but are they traveling the same speed in the glass?
Given your observations which one travels more slowly in glass? (Check your reasoning with your TA). Hint: remember the concrete/sand (or mud) interface to infer how the amount of bending depends on the difference in speed as the trucks (light) go from air to the glass and the glass back to air. Basically what is happening is that the glass bends light of different wavelengths (colors, frequencies) by slightly different amounts which is equivalent to saying the light of different wavelengths travels at slightly different speeds through the glass. This phenomenon is put to good use in a prism when one wants to disperse the different colors of white light. It is also the cause for a rainbow. 3) For a given lens the focal length for red light (f red ) is a little different from that for blue light (f blue ). Which is larger: f blue or f red? Is the difference large? Additional Experiment Think up an additional experiment using the equipment from this lab and try it, recording the results in your lab book. Additional Question A diverging lens does not produce a real image from a real object. How would you determine the focal length of a diverging lens? You can use additional lens if needed.