Experiment 6: Constructing a Microscope

Transcription

1 Experment 6: Cnstructng a Mcrscpe Pre-lab Preparatn: Revew the llwng sectns rm the Yung an reeman textbk page reerences gven r th etn: Sectn 3.: Thn Lenses, p. 7 8 Sectn 3.7: The Magner, p Sectn 3.8: Mcrscpes an Telescpes, p. 9 9 Cmplete questn 3.08 rm the textbk Rea the vervew belw, an rughly plan hw t cnstruct a mcrscpe Overvew: Usng a cnvergng lens, t s pssble t rm a real r magnary mage, epenng n where the bject s place relatve t the lens. In the case where the bject s place utse the cal length the lens, an nverte, real mage s rme: bject real mage ptcal axs gure : Real mage rmatn by cnvergng lens In gures,, an 3, the cal length the cnvergng lens s, the stance t the bject s, an the stance t the mage s. Cnversely, r the case where the bject s place nse the cal length, a larger, uprght, vrtual mage results, magnyng the bject, as epcte n gure 3, n the next page. A specal case ccurs when an bject s place at the cal pnt: bject gure : Image rmatn at nnty r bject at cal pnt r cnvergng lens The technque r rawng ray agrams s revewe n Sectn 3. p. 79 the textbk. The three prncpal rays epcte n gs.,, an 3 are: a ray travellng parallel t the ptcal axs gets reracte thrugh the ar cal pnt, a ray travellng thrugh the near cal pnt gets reracte parallel t the ptcal axs, an a ray travellng thrugh the lens centre es nt get reracte. Where the rays emtte rm the bject ntersect s where the mage s rme.

2 vrtual mage bject gure 3: Vrtual mage rmatn by cnvergng lens When the bject s lcate at the cnvergng lens cal pnt, as n gure, the rays rmng the mage are parallel; thus, an mage nnte lnear magncatn s rme. Ths behavur s quante by the thn lens equatn, relatng the bject stance,, the mage stance,, an the cal length the lens: 0 Ths equatn s erve n Yung an reeman, th Etn, p usng a smlar trangles argument. The sgn cnventn use by the textbk stpulates that > 0 r a cnvergng lens, an > 0 the mage s rme n the ppste se the lens as the bject.e. a real mage. The behavur n gure s bserve >, gvng > 0. Cnversely, <, then < 0, gvng the vrtual mage llustrate n gure. nally,, then t gve / 0. Next, tw types magncatn may be ene: the lnear r lateral magncatn, an the angular magncatn. The lnear magncatn, m, s the negatve rat the bject s heght t the mage s heght: m h h Makng use smlar trangles n the prevus gures gves that the lnear magncatn s als the rat the mage stance t the bject stance: m I ne slves r n the thn lens equatn, Eq., an substtutes t nt the expressn r lateral magncatn, Eq., then: m 3

3 Hence, an bject s place at the cal pnt,, the lateral magncatn appraches nnty, as nte earler. It s clear, hwever, that placng an bject at the cal pnt a magnyng glass es nt pruce an mage the bject that s nntely large, s an alternate measure magncatn must be ene. Ths s where the angular magncatn s useul. The angular magncatn, M, s ene as the rat the angles subtene by the bject an ts magne mage: θ bject θ usually ene as 5 cm parallel rays cuse by eye bject gure : Cmparsn angle subtene by bject an magne bject θ M θ tan h tan h / / r small angles θ an θ, tanθ θ an tanθ θ, leavng the llwng expressn r the angular magntue: M r cnvenence an cnsstency, mst mcrscpes ene angular magncatn wth 5 cm, the mnmum stance rm the eye at whch bjects can be reslve r mst peple. It can be seen that, n prncple, as the cal length appraches zer, the angular magncatn appraches nnty. The magncatn s actually lmte by eects such as wavelength-epenent nex reractn an rregulartes n the shape the lens that make the mage rreslvable r M > 5 r s. T aress ths, a cmpun mcrscpe, makng use tw cnvergng lenses, s cnstructe: eyepece D bjectve lens D gure 5: Sample mcrscpe apparatus 3

4 D eyepece bjectve lens D gure 6: Alternate sample mcrscpe In bth gures 5 an 6, the bjectve lens, the cnvergng lens wth cal length, s place clsest t the bject, an pruces a real, nverte mage the bject at stance. Ths real mage s then magne, ether by puttng t nse the cal length,, the eyepece as n gure 5, r rght nse the cal length as n gure 6. One multples the lnear magncatn each lens t n the ttal magncatn the system n the case gure 5, but r gure 6, the lnear magncatn the eyepece appraches nnty, s the magncatn s the pruct the lnear magncatn the bjectve lens, an the angular magncatn the eyepece. These expressns are gven belw: D µ mm g. 5 e 5 mm g. 6 e 6 µ D s the stance between the eyepece an the real mage pruce by the bjectve lens, whch can be un by cnserng the stance between the bjectve lens an the actual bject,, an applyng the thn lens equatn, Eq.. Prceure The gal ths experment s t cnstruct a mcrscpe an quanty ts magncatn actr. The necessary ngreents, nclung three cnvergng lenses, a lght surce, a screen, an ptcal bench, an varus hlers, wll be mae avalable. The three lenses have unknwn cal lengths that must be un expermentally by any meth ne ns practcal. r plannng purpses, t may be assume that the lenses have cal lengths apprxmately 5 cm, 0 cm, an 5 cm. Once the cal lengths are knwn, the mcrscpe may be create, usng the arrangement n gure 6 r 7 as a rugh gue. The magncatn the mcrscpe must be measure, smehw, s sme thught must g nt ths. Attemptng questn 3.08 rm the textbk wll help n esgnng the mcrscpe an enng the magntue. Snce ths lab esn t specy a partcular prceure t llw, a ull wrte-up s warrante. Arrange the wrte-up wth sectns lke the nes gven belw: Abstract: summarze the gal an results the nvestgatn n a ew sentences. Intructn: let reaers knw what yu set ut t, an brely gve sme general backgrun n thn lenses. Mre than a ew paragraphs r ths sectn are nt necessary.

5 5 Meth: ths sectn s mprtant speccally explan, wth numbers an agrams, hw yu measure the cal length the lenses, hw yu assemble the mcrscpe, an hw yu measure the magncatn the mcrscpe. Results: summarze the analyse an prcesse results yur nvestgatn, nclung the cal lengths the lenses, the mensns the mcrscpe, an the magncatn. Make sure t nclue uncertantes r each the reprte quanttes, an cmpare bserve values t theretcal equvalents wherever pssble. Shw calculatns n a separate sectn r appenx yu want. Errr Analyss: ths sectn s als mprtant r ths lab, a rmal, quanttatve treatment errr s necessary. Prpagate errr rm measurements t calculate values usng the general rmula, r a sample quantty x,y: y y x x 7 In Eq. 7, s the errr n the calculate value, whch reles n tw measure quanttes, x, an y, wth relate uncertantes x an y, respectvely. r example, the errr n the cal length s relate t the errr n the bject stance an the mage stance by the llwng:, Thus, the cal length s a tw-varable equatn, as n Eq. 7. The requre partal ervatves are: I these are substtute nt the equatn r the uncertanty, then: 8 Hence, by estmatng the errr n the pstn the bject,, an the pstn the mage,, the crrespnng errr n the cal length,, s un r that measurement. Nte that, r the cal length measurement r the lenses, yu wll want t average several values r. Calculatng the uncertanty asscate wth each measurement,, allws values wth large uncertantes

6 t be scare. The uncertanty n the average cal length value may then be rughly estmate by the llwng a-hc rmula: avg... N N average avg 9 N Thus, the errr n the average cal length value s gven by the average the errr n the nvual values, ve by the rt the number values examne, N. Estmatng the errr n the magncatn r the mcrscpe, gven by an equatn lke Eq. 5 r 6 may be ne n the same way as was emnstrate r the cal length, Eq. 8. Make sure t cmment n surces errr an justy the measurement uncertantes n each case. r sme measurements, the uncertanty may be larger than hal the smallest vsn n the measurng evce explan why n each case. Cnclusn/Dscussn: brely summarze what was un an restate the numbers an ther asscate uncertantes. Mentn partcularly prblematc parts the nvestgatn, an suggest ways that the prceure may be mprve, smene were t try an repeat yur experment r better results. Cnclusn: G luck! The trcky part ths nvestgatn wll lkely be nterpretng the ata that s cllecte. Perrmng the actual experment shul nt be t cult, but a bt careul thught must g nt plannng what t t get useul ata, an what t wth the ata nce t s been cllecte t get useul cnclusns. Ths apprxmates research, where much ert ges nt plannng an justyng experments, an tryng t learn thngs rm them, as ppse t actually perrmng the experments. Accrngly, the mark r ths nvestgatn wll be base mre n ne s ablty t create an justy an expermental prceure, an quanty the results an uncertantes, as ppse t gettng the crrect results keep that n mn! Strctly, ne shul n the weghte mean the -values, wth the weghtngs beng nversely prprtnal t the uncertanty r each value; that s, w /. T save tme, the errrs are abut the same r each value, ne can take the stanar mean an estmate the uncertanty n the average value usng Eq. 9. 6