Thin Lenses. Consider the situation below in which you have a real object at distance p from a converging lens of focal length f.

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1 Thin Lenses Consider the situation below in which you have a real object at distance rom a converging lens o ocal length. Lens Object Image I > then a real image o this object will be roduced at distance rom the lens on the oosite side. These uantities are related by the thin lens euation 1 = (1) and sign conventions are given in the table below. (+) or real objects ( ) or virtual objects (+) or real images ( ) or virtual images (+) or converging lens ( ) or diverging lens The ratio o the image height i to the object height o is the magniication, which is euivalent to the ratio o image distance to object distance. m = i o = (2) I m < 1 the image is smaller that the object; an image larger than the object means m > 1. As or sign, m is ositive i the image is oriented the same as the object and negative i the image is inverted. For diverging lenses, the situation is a little more comlicated - these lenses roduce virtual images o real objects. However, they do roduce real images o virtual objects. Consider the situation below. 1

2 Lens Object Image This starts the same as beore. However, a diverging lens o ocal length is then laced between the converging lens and the location o its image. The diverging lens now uses this image as a virtual object, roducing a real image on the same side o the lens. As beore, is the distance rom object to lens and rom image to lens. The sign conventions hold or diverging lenses as well. Aaratus Dynamics track, Object box (light source), Lens holders, Image screen, Converging lens, Diverging lens, Meter stick, Rule. Procedure Converging Lenses 1. Place the image screen at one end o the track and the converging lens in the middle. Rotate the track on the table so that it is ointed at a distant lighted object (at least 5m away); this is shown in Figure 2. Adjust the location o the lens until the distant object is in ocus on the screen. Record the distance d rom the lens to the screen. Figure 1: Finding the distance d. d 2. Return the track to the middle o the table and lace on it the object box, the converging lens, and the screen as shown in Figure 3. For maximum lexibility, ut the object box very near the end o the track, and leave it there. 3. Adjust the osition o the converging lens so that it is at least distance d away rom the object box but less than 2d. Now, adjust the osition o the screen until you get a clear image. Measure,, and i (o is ixed) or this arrangement. Place the values in the irst column o Table 2 and 2

3 Figure 2: Focal length o the converging lens. comlete the remaining calculations. Your image descrition should be: real or virtual; erect or inverted; larger, same size, or smaller. 4. Reeat Ste 3 or distances between object box and lens o 2d and greater than 2d. o i m d < < 2d = 2d > 2d Descrition o Image Table 1: Data or Converging Lens Diverging Lenses Euation 1 works or diverging lenses as well, but unortunately they roduce virtual images o real objects. Thereore, we will need a dierent rocedure. Diverging lenses do roduce real images o virtual objects, so you will use a converging lens to roduce an image that will be used as the object or a diverging lens. It will then roduce a real image. 1. Place the converging lens between the object box and the image screen and obtain a clear image, as was done in the revious rocedure ( > 2d works well). Record the necessary data or this lens in Table 3 and comlete the remaining calculations. Beore moving on, record the actual osition o the screen on the track below. Screen location 3

4 2. Place the diverging lens between the converging lens and the screen as shown in Figure 4. Adjust the location o the diverging lens and/or the location o the screen (only!) until you again have a clear image. This may take some doing until you have an image that is usable. Figure 3: Focal length o the diverging lens. 3. Record the necessary data or the diverging lens and comlete the remaining calculations. Remember that you are using the image rom the converging lens as the object or this lens, so i converging = o diverging As always, object distance is rom object to lens, so here it is rom the screen location you noted in Ste 1 and the diverging lens. o i m Converging Lens Diverging Lens Descrition o Image Table 2: Data or Diverging Lens Analysis Converging Lenses 1. There are two dierent euations or calculating the magniication o the lens. Which did you use? Why? 4

5 2. Can you make any statements concerning magniication and object distance? 3. What would the object distance have to be in order or the image to be roduced exactly at the ocal length o the lens? In other words, when is the only time =? (This is why you had some variance in your calculated ocal lengths.) Diverging Lenses 1. Using the original object (object box) and the inal image on the screen, calculate the magniication o the two-lens (converging + diverging) system. 2. How is the magniication o this two-lens system determined using the individual magniications o each lens? 5

6 Pre-Lab: Thin Lenses Name Section Answer the uestions at the bottom o this sheet, below the line - continue on the back i you need more room. Any calculations should be shown in ull. 1. Give the sign conventions or converging and diverging lenses (i,,,, and m). 6