Experiment 3 The Simple Magnifier, Microscope, and Telescope Introduction Experiments 1 and 2 dealt primarily with the measurement of the focal lengths of simple lenses and spherical mirrors. The question of lateral magnification, given by m = s /s = i/o, follows logically. In some cases (typically with telescopes) the object distance is functionally infinite, at which point this expression fails, so the angular magnification (ratio of subtended angles) is used instead. In Experiment 3, you will deal with a number of optical instruments in which the near point of the eye (taken as 25 cm for the average middle-aged white male physics professor writing an optics textbook) is a crucial aspect of the measurement. Chapter 10 of Jenkins and White covers optical instruments and useful material can be found in Chapter 6 of P.P. 1 The lab will cover the simple magnifier, microscope, various telescopes, the concept of exit pupil, and limits on the resolving power of a given optical instrument. In 6 6 of P.P., there is a useful discussion of the exit pupil and the measurement that allows an alternate determination of the lateral magnification in various optical instruments. Your full understanding of the resolving power formula given below will await your later exposure to the topic of diffraction effects in Physics 322/422 (which you probably have already taken). Chapter 15 in J.W. may be read to get the flavor of the topic. When you think of magnifying devices you may think of the Sherlock Holmesstyle single lens or a two- or three-lens microscope or telescope. The operation of the single lens magnifier is straightforward, but the multiple-lens systems are a bit more complex. The systems we ll be using as examples this week have two lenses the eyepiece (also called the ocular) and the objective. The role of the objective lens is to form an image at the focal plane of the eyepiece. In addition to magnifying, this has the added benefit that the final image (what your eye sees) is formed at infinity (recall the lens equation we used previously, and remember that the object for the eyepiece is at the focal point), which greatly reduces the strain on the eye s muscles as it doesn t need to focus on an image very close to it. 1 Simple Lens Procedure The purpose of this part is to compare the magnification of a simple lens to theory. There are 3 lenses of focal lengths 5, 10, and 25 cm. You will measure their magnification. Keep in mind that a simple magnifier is defined in terms of altering the near point of the eye. Thus, we can focus on an object at a distance less than we normally could and hence the object looks bigger. This is how you will measure magnification. 1 F.L. Pedrotti and L.S. Pedrotti, on reserve in the Physics Library. 1
Figure 1: Magnifier Setup Place a (5, 10 or 25 cm) lens in front of the periscope. Place a meter stick in the focal plane of the lens. Record the distance of the meter stick to the lens. This is f. Use the image of the meter stick as seen through the periscope to measure the size of a fixed distance on the meter stick as seen through the lens. This is hard to explain; see the diagrams. I will try to explain what we are doing. Let s take a fixed distance on the meter stick, for example 1mm. We will call that h. Now we can see h through the lens. We can also see an image of the meter stick through the periscope. The images should be superimposed. Now we use the periscope image of the meter stick to measure h. We will call this value H. Record h and H. Record the total distance from your eye through the periscope to the meter stick. We will call this D. Do this for each of the 3 lenses you are given (f = 5, 10 and 25 cm). Analysis The theory 2 says that the angular magnification of a simple lens is just, M = 25cm/f for an object one focal length away from the lens. From the 2 see Jenkins and White, Sec. 10.8 2
Figure 2: Magnifier Concept figure, we can see that the angle subtended by the image h is just h/f. Call this θ. We also see that the image of h as seen through the lens and measured with the periscope subtends an angle θ = H/D (small angle approximation). These two angles are equal because the images are superimposed. We are using the periscope image to measure the angle subtended by h as seen through the lens. Now, by definition, the angle subtended by h without a lens is θ = h/25cm. The magnification therefore is M = θ /θ. θ = H D = h f f = hd H θ = h/25 M = θ θ = (H/D) (h/25cm) = 25cm H hd So our measured magnification is M = 25cm H/hD and our theory value is M = 25/f. Compare this theory to what you measured. 2 Microscopes Procedure In this section you will be looking at microscopes. Keep in mind, that the difference between a microscope 3 and a telescope 4, is that the microscope focuses on things very close to the focal point of the objective, and the 3 see J.W., 10.11 4 see J.W., 10.13 3
telescope focuses on things very far away. Additionally, microscopes are generally constructed by specifying the distance between the objective and eyepiece lenses, and then moving the entire apparatus to achieve focus. You will use a 5 and a 10cm lens to make a microscope. Figure 3: Microscope Place the 10cm lens (eyepiece) on the optical bench. Now place the 5cm lens (objective) about 28cm from the eyepiece. Next place a short ruler 10cm beyond the objective lens. Note that this should put the image of the meter stick in the nearest focal plane of the ocular (eyepiece). Place a screen in the focal plane of the eyepiece between the two lenses. This is 10cm from the 10cm lens. Illuminate the meter stick with a flashlight. You should see an image of the meter stick on the screen. Adjust the position of the meter stick (not the lens or screen) until you get a sharp focus on the screen. Pick some fixed distance on the meter stick such as one centimeter. Call this h. Now measure the size of the image of h on the screen. Call this h. Record h and h. Measure the distance from the meter stick to the objective lens and call this d. 4
Measure the distance from the objective lens to the screen and call this d. Record d and d. You have just measured the magnification of the objective lens. Remove the screen from the focal plane of the eyepiece. Look through the 10cm eyepiece. You should see an image of the meter stick. The microscope should be in focus in order to observe a well-focused image. Next place the periscope in front of the eyepiece. Adjust the periscope until you can see an image of the meter stick. Again, pick a fixed distance on the meter stick called h. Measure h with the superimposed image in the periscope. Call this H. Measure the total distance from your eye through the periscope to the meter stick. This is D. Measure the distance from the eyepiece to the objective, this should be 28cm. Now switch the objective and eyepiece lenses and repeat this procedure. Analysis Compare your results to theory. These measurements are heavily dominated by bias, so error based on the precision of your measurements is most likely not going to be sufficient to cover a difference between results and expectations - more for you to discuss in your report. For the first part, the magnification of a simple lens is m = i/o or in our case m = d /d. The experimental magnification is m = h /h. For the second part the theory is M = 25cm x/(f 1 f 2 ), where x is the separation of the focal points. That is, x = (the separation of the lenses - (f 1 + f 2 )). The experimental magnification is given by M = (H/D)/(h/25 cm) = 25cm H/hD (the same as a simple magnifier). 3 Telescopes Procedure The next three sections deal with telescopes. There are 3 basic types. The astronomical or Keplerian 5 and Galilean designs use two lenses (an objective lens, and a positive focal length eyepiece for the Keplerian, and a negative focal-length eyepiece for the Galilean), while the Newtonian 6 uses a mirror as the objective. First we will deal with the Galilean telescope. Place a 50 cm lens in the middle of the optical bench. This lens is the objective. Place a 20 cm, the eyepiece, about 30 cm behind the objective lens, so that the focal points are roughly at the same place. 5 see J.W., 10.13 6 see Hecht and Zajac, p.155 5
Figure 4: Galilean Telescope Now place a meter stick on the wall on the other side of the room. Move the eyepiece lens until the meter stick on the opposite wall is brought into sharp focus. Now place the periscope behind the eyepiece and adjust it until you can see the meter stick on the other side of the room. Move your head and adjust the objective at the same time until there is no parallax between the two images of the meter stick. Make a direct comparison of the two images and find the magnification. Next you will set up an astronomical telescope. positive objective and a positive eyepiece. This instrument uses a Replace the 20cm eyepiece with the +20cm eyepiece. Measure the distance from the objective to the meter stick (it shouldn t have changed unless you moved it). The analysis for this is very similar to that for the Galilean telescope. Let s call the angle subtended by the unmagnified image in the periscope φ 1, and by the magnified image in the telescope φ 2. The magnification is therefore given by M = φ 2 /φ 1. Finding φ 1 is easy - the size of your image 6
Figure 5: Astronomical Telescope (say, 5 cm) divided by the distance from your eye to the far wall. Find φ 2 by dividing the apparent (magnified) size of the object by the distance between the far wall and the objective (the additional distance of the length of the telescope is generally insignificant, but this is an opportunity to see how effective this approximation is. What percent difference does this make?). 4 Resolving Power Procedure This last section of the lab is meant to investigate the fundamental limitation of any magnifying device - its ability to distinguish two closely-spaced objects. Place the set of slits on one end of the optical bench on the mercury lamp. We ll look at three different slit widths. Next place the small telescope on the bench as close as you can to the slits while still getting it to focus (about 60 cm). This is the telescope mounted on the rod. Now you will be given a brass aperture. Place it in front of the objective of the telescope (it doesn t really mount properly, so make sure it sits properly and doesn t fall off). Record whether or not you can still resolve the slits. 7
Move the telescope back by 10 cm. Are the slits still resolved? Keep looking through the telescope back by 10 cm steps and seeing if you can resolve the slits until the telescope is at the other end of the optical bench. Analysis Calculate the angular resolving power of the aperture by θ r = 1.22λ/D. Compute the angular separation of the slits at each step by θ = w/l, where w is the width of the slits and L is the distance from the slits to the telescope. Compare to theory. The table of theoretical angular resolving powers should tell you at what distances the slits should be resolved and at which should not. Is this confirmed by your observation? The wavelength of the green mercury light is λ = 5461 Å. 8