Lab 10 Thin Lenses What Yu Nee T Knw: The Physics Frm last week s lab, Reflectin an Refractin, yu shul alreay be familiar with the fllwing terms: principle axis, fcal pint, fcal length, f, cnverging lens (f +), an iverging lens (f ). If these cncepts aren t fresh in yur hea, then review last week s lab. This lab will be using these cncepts t shw yu hw t frm images with thin lenses. When frming an image, there will always be an bject that the lens is using t create the image. Fr example, glasses r cntacts are lenses that frm images that yur eyes are able t fcus n. The bject wul be anything in yur fiel f view. Anther example wul be when yu see a mvie in a theater. Yu are lking at an image that is frme n a screen by a lens in the prjectr. (In fact, the first part f this lab yu will be creating this exact situatin.). Fr this situatin, the bject wul be the film in the prjectr. In iagrams, like Figure 1, bjects are rawn as arrws. There are tw ways in which yu can gather infrmatin (such as the size r rientatin) f the image. There is a light-ray iagram apprach an an algebraic apprach. Figure 1 shws a light ray iagram fr an bject that is utsie f the fcal pint f a cnverging lens. The meth use t raw this iagram will be left t the lecture class t explain. This lab will nly be cncerne with the algebraic apprach. i OBJECT f f IMAGE FIGURE 1 - Light ray iagram There are tw main equatins that will tell yu infrmatin abut the image. The first is calle the Thin Lens Equatin. Refer t Figure 1 n hw the variables relate t the iagram. 1 f = 1 + 1 i f is the fcal length f the lens (in cm) is the bject istance (in cm) i is the image istance (in cm) Given a fcal length an an bject istance, yu can use the Thin Lens Equatin t calculate the image istance. The sign f the image istance can tell yu aitinal infrmatin n the image. See the Sign Cnventins area n the next page. 10-1
There are ther ways in which yu can tell if an image is real r virtual. If yu can frm an image n a screen r a wall then it is real image. A g example f a real image is the image yu see n a screen in a mvie theater. On the ther han, if yu have t lk thrugh a lens t see the image, then it is a virtual image. Peple wh wear glasses r cntacts are lking at virtual images. The secn equatin yu will use in this lab is the Magnificatin Equatin i m = m is the magnificatin f the image (n units) i is the image istance (in cm) is the bject istance (in cm) There are several things that the magnificatin can tell yu abut the image. See the Sign Cnventin chart belw. Sign Cnventins fr Lenses If i is + then the image is real. If i is then the image is virtual. If m is + then the image is upright. If m is then the image is inverte. If m > 1 then the image is larger than the bject. If m < 1 then the image is smaller than the bject. S, in re-examining Figure 1 an using the infrmatin in the chart abve, yu can tell that the magnificatin f the image must be negative an less than 1. In tay s lab yu will be using all f the abve infrmatin t calculate, in a variety f ways, the fcal lengths fr a cnverging lens an a iverging lens. The Setup The main piece f equipment yu will be using is an ptical bench. See Figure 3 n the next page. The bench will hl a light surce, ne r tw lenses in lens munts, an a screen. The light surce is the same light bx yu use last week. Hwever, this time yu will use the ppsite sie f the bx, which has a pattern, like Figure 2, n an paque piece f plastic. Light will shine thrugh the plastic an serve as the bject fr the ptical system. Yu are able t mve the lens munts an the screen back an frth n the track f the ptical bench. This will allw yu t frm images n the screen. The arrws n the bject in Figure 2 will let yu knw if the image has change its rientatin with respect t the bject. NOTE: DO NOT WRITE ON THE SCREEN. FIGURE 2 - Object n light surce h 10-2
LIGHT SOURCE SCREEN LENS LENS MOUNT What Yu Nee T D: FIGURE 3 - Optical bench an accessries. Fcal Length an Infinity Fr the first part f the lab, yu will nt be using the ptical bench. Instea yu will g t the wall near the rear r f the labratry. Bring with yu the munte cnverging lens (the ne with +200 mm n it) an a ruler. Yur TA will raise the blins f the winw irectly acrss frm the wall. The light cming frm the winw will be yur bject. This light is cnsiere t be cming frm very far away. Using the cnverging lens, try t fcus an image f the trees utsie f the winw n the wall. Yu might be able t get yur TA t wave his arms arun (an maybe jump up an wn) in frnt f the winw s that yu can see hw this situatin relates t a mvie theater. Ntice that this is a real image. When yu have a fcuse image, use the ruler t measure the istance frm the wall t the lens. The lens is psitine at the center f the munt s yu shul use that as a reference pint when yu make yur measurement. The istance that yu are measuring is the image istance, but in this specific situatin it is als the fcal length f the lens. This fcal length is yur first piece f ata. Questin #1 Using an equatin frm the intructin f this lab, explain why the image istance is apprximately equal t the fcal length in this situatin. i f m i i = h h i h h m = % errr fr m 1 st lcatin 2 n lcatin Average fcal length: % errr fr fcal lengths: CHART 1 The Optical Bench Make a cpy f Chart 1. Yu are nw ging t use the ptical bench t measure the fcal length f the same lens yu use at the wall. First, make sure that the light surce is flush with 0 cm n the ptical bench. Yu shul leave it that way fr the entire lab. The screen shul be place at 110 cm. Plug in the light surce. Measure the height, h, f the arrw (yur bject ). See Figure 2. Place this value in bth rws in the chart. Place the cnverging lens/munt n the ptical 10-3
bench in between the bject an the screen. There are tw lcatins fr the lens alng the ptical bench that will fcus an image n the screen. Fin ne f these lcatins. Once yu have the image in sharp fcus, take measurements fr the bject istance,, the image istance, i, an the height f the image, h i. NOTE: Yu will be able t fcus a sharper image if yu turn ff the lamp at yur table. Place these values in the chart. Repeat this prceure fr the ther lcatin that frms an image. EQUATIONS 1 1 1 = + f i i m = A) Using the abve ata fr bth lcatins, calculate the fcal length f the lens. Take the tw fcal lengths an average them. Cmpare, by calculating a percent errr, this average value t the fcal length yu measure at the wall. Place all values in the chart. B) Using the values, calculate the magnificatin fr each lcatin. Place these values in the chart. Fin the pruct f the tw magnificatins. NOTE: Ignre any negative signs. The value shul be very clse t 1. Questin #2 Why shul the pruct f magnificatins be equal t 1? Questin #3 Discuss the state f the image fr ne f the lcatins. Cmment n such things as real/virtual, upright/inverte, an bigger/smaller. Des the state f the image match with the calculate values? Explain!!! Discuss!!! C) Yu can als calculate the magnificatin by iviing the image height by the bject height, m = h i /h (n Seven Dwarfs jkes please.) NOTE: There is n aitinal negative sign in this equatin. Using this equatin, calculate the magnificatin at each lcatin. Calculate a percent errr with its sister measurement frm Part B. NOTE: Take the abslute values f the magnificatins befre yu yur percent errr. Place all values in the chart Diverging Lens Nw yu are ging t measure the fcal length f the iverging lens. Yu can t frm a real image n a screen with just a iverging lens. G ahea an try it. Remve the cnverging lens an put the iverging lens n the bench. (The iverging lens munt has brass screws n it.) Slie the lens back an frth t frm an image. Yu can t. By itself, a iverging lens can nly frm virtual images. Yu can lk thrugh the lens an see a virtual image but yu can t frm a real image with it. In rer t get a real image t frm n the screen yu have t use a cmbinatin f tw lenses. Put bth lenses n the ptical bench. The rer f the munts shul be: OBJECT CONVERGING LENS - DIVERGING LENS SCREEN. There are many pssible psitins f the tw lenses that will allw yu t frm an image n the screen. S, by trial an errr, get an image t frm n the screen. Just slie bth munts arun until yu get an image. If yu can t get an image t frm then grab yur TA. Nw take the fllwing ata [See Figure 4 n the next page fr reference. NOTE: Drawing is nt t scale.] Measure the istance frm the bject t the cnverging lens, 1. Measure the istance frm the cnverging lens t the iverging lens,. Measure the istance frm the iverging lens t the screen, i2. Measure the height f the image, h i. 10-4
i2 1 2 DIVERGING LENS OBJECT CONVERGING LENS IMAGE 1 IMAGE 2 (n the screen) i1 FIGURE 4 - Tw lens set-up EQUATIONS 1 1 1 = + f i i m = A) The first thing yu nee t is calculate the image istance, i1, fr the cnverging lens. See Image 1 in Figure 4. This is the image that wul frm if the iverging lens weren t there, that s why it s graye-ut in Figure 4. Using yur 1 an the average fcal length fr the cnverging lens (frm the first part f the lab), calculate i1. In rer t calculatins fr multiple lens systems yu have t treat the image fr the first lens as the bject fr the secn lens. That s why 2 is labele the way it is in Figure 4. (The bject istance is frm Image 1 t the secn lens.) B) Using the ata yu tk, calculate 2 base n the Figure 4. OK, Image 1 is nw cnsiere t be the bject fr the secn lens (call it Object 2). The light that is trying t frm Image 1/Object 2 is entering the iverging lens frm the left. Since Object 2 is n the ppsite sie f the lens that the light is cming frm, it is cnsiere t be a virtual bject. Any virtual bject has a negative value s make sure yu use a negative in the calculatin belw. C) Using yur ata, calculate the fcal length, f 2, f the iverging lens. Cmpare this fcal length t the ne given n the lens munt. Use a percent errr. Questin #4 Is the value yu calculate in Part C cnsistent with what yu knw abut the fcal length fr a iverging lens? D) Each lens has its wn - i pair f ata. Using this ata, calculate the magnificatin fr each lens. Label them m 1 an m 2. E) The ttal magnificatin fr a multi-lens lens system is the pruct f the separate magnificatins. Fin the ttal magnificatin (inclue any negative signs). Questin #5 Is the ttal magnificatin f the system cnsistent with the rientatin f the image (inverte r upright) n the screen? Explain. F) We shul als be able t calculate the ttal magnificatin f the system by using the equatin, m = h i /h. Calculate the ttal magnificatin with this equatin. 10-5
G) Calculate a percent errr, cmparing the magnificatins frm Part E an Part F. Nte: Take the abslute values f the magnificatins befre yu yur percent errr. What Yu Nee T Turn In: Make sure any measurements yu mae are in the apprpriate sectins where yu were aske t measure them. Turn in yur chart that has any measurements r calculatins inclue in it. Make sure any calculatins are ne in the apprpriate sectins. Yu nly have t ne sample calculatin fr each ifferent type. 2008 by Michael J. Dubuque 10-6