Experiment 3 The Simple Magnifier, Microscope, and Telescope

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1 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 s. The question of lateral magnification, given by m = s /s, follows logically. In Experiment 3, you will deal with a number of optical instruments in which the near point of the eye 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. Chapter 15 in J.W. may be read to get the flavor of the topic. 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 25cm. 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. Place a (5, 10 or 25cm) 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. 1 F.L. Perdotti and L.S. Perdotti, on reserve in the Physics Library. 1

2 Simple Magnifier Setup half-silvered f + Lens Meter Stick Figure 1: Magnifier Setup Simple Magnifier Concept observer θ' H (length of h as measured through periscope) D θ' h lens f Meter Stick Figure 2: Magnifier Concept 2

3 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 = 25/f for an object one focal length away from the lens. From the 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. And the magnification is M = θ /θ. θ = H D = h f f = hd H θ = h/25 M = θ θ = (H/D) (h/25) = 25H hd So our measured magnification is M = 25H/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 telescope focuses on things very far away. You will use a 5 and a 10cm lens to make a microscope. Place the 10cm lens (eyepiece) on the optical bench. Now place the 5cm lens (objective) 28cm from the eyepiece. Next place a plastic 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). 2 see Jenkins and White, Sec see J.W., see J.W.,

4 Microscope Setup f 1 x f 2 d half-silvered eyepiece screen objective Meter Stick Figure 3: Microscope 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 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. Use a metric tape. Call this h. Record h and h. Measure the distance from the meter stick to the objective lens and call this d. 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 well focussed image. 4

5 Next place a 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. A simple percent difference is what we want here. These measurements are too crude to allow much in the way of error analysis. 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 = 25x/(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) = 25H/hD (the same as a simple magnifier). 3 Telescopes Procedure The next three sections deal with telescopes. There are 3 basic types. They are the astronomical (Keplerian) 5, Galilean, and Newtonian 6. First we will deal with the Galilean telescope. This instrument uses a positive objective lens and a negative ocular. Place a 50cm lens in the middle of the optical bench. This lens is the objective. Place a 20cm, the ocular, about 30cm behind the 50cm lens. Now place a meter stick on the wall on the other side of the room. Move the 20cm lens until the meter stick on the opposite wall is brought into sharp focus. 5 see J.W., see Hecht and Zajac, p.155 5

6 Galilean Telescope f 1 f 2 f 1 f 2 half-silvered - lens ocular + lens objective Meter Stick on far wall Figure 4: Galilean Telescope 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. This instrument uses a positive objective and a positive ocular. With the meter stick still on the wall, place a 19.3cm achromatic lens in the middle of the optical bench. A measuring eyepiece will be used as the ocular. Nowplaceaneyepiecebehindthelens. Theeyepiecehasafinescaleinside. The ocular is a 6 power eyepiece, thus the focal length is (25/6)cm. Measure the distance from the 19.3cm achromat to the meter stick. With the scale in the eyepiece, measure the image of the meter stick. That may sound a little strange. To make it clear, say we take a set distance on the meter stick, from say the 25cm mark to the 30cm mark. Then the objective lens of the telescope will form an image of this section of 6

7 Astronomical Telescope f 2 f 1 positive ocular objective Meter Stick on far wall Figure 5: Astronomical Telescope the meter stick and it will have some size. Measure this image with the scale in the eyepiece. Note, the distance on the meter stick (5cm in this example) subtends an angle as measured from the 19.3cm lens, which is 5cm divided by the distance from the 19.3cm lens to the meter stick. This is the angle φ 1 in the equation M = φ 2 /φ 1. The distance that we measure on the scale in the eyepiece, divided by the focal length of the eyepiece is just φ 2. Thus by this method we have directly measured the angular magnification of the telescope. 4 Resolving Power Procedure This is the last section of the lab. Place a pair of slits on one end of the optical bench. Place the mercury lamp behind the slits. Next place a small telescope on the other end of the bench. This is the telescope mounted on the rod. Now you will be given a set of apertures. Focus the telescope on the slits and place each aperture in front of the objective of the telescope in turn. Record whether or not you can still resolve the slits. 7

8 Record the distance from the objective to the slits and the separation of the slits. Measure the diameter of each aperture. Analysis For each aperture calculate the angular resolving power by α = 1.22λ/D. Compute the angular separation of the slits. Now compare to theory. The table of theoretical angular resolving powers should tell you which aperture allowed the slits to be resolved and which did not. Is this confirmed by your observation? The wavelength of the green mercury light is λ = 5461Å. 8