How do microscopes use lenses? Exploring Light and Lenses Introduction OPTICSthe sub-eld of physics focnasing on the stud)r of lightis important to many areas of biology and engineering. The use of optics in biologyr has evolved from the simple light microscope used by Darwin to the complex, livecell, high mlution microscope used in current cuttingedge research. In engineering and ecology, the use of binoculars, cameras, and surveying scopes have followed suit. in this two-week lab, we will be exploring how lenses can help us create images of small or distant objects. While contemporary microscopes and telescopes usually,r combine multiple lenses together, we will be exploring single-lens systems we are only beginning to learn about light. Your task is two-fold: 1) Design a way of determining the focal lengths, f, to high precision for ve converging lenses. and 2) Design an experiment to determine a mathematical relationship between the focal length, f, the image distance, 5\The image distance S; is the distance from the image (where you would place your eye) to the lens. The object distance, So , is the distance from the object to the lens. For most microscopes, telescopes, etc., the object location and image location cannot be changed (they are a fixed distance apart, L) so it is the type of lens and the position of the lens that are changed in order to achieve different magnifications and to focus the image. Your goal should be to develop a quantitive model-that is, a mathematical relationship that describes your data. This is most easily done by having a spreadsheet program like Excel generate a "best fit line." Don't forget to continue applying the methods from last week to identify, assess, and reduce uncertainty and new methods introduced in this lab to build statistical confidence in your results. For Your Report: Unlike last week, you and your group will need to collaborate on writing a formal report. This re- port should include careful discussions of (a) your methods/procedures for finding the focal lengths and for investigating the f/So/S;/L relationships-this should include your methods for identifying and reducing uncertainty; (b) Your data and a quantification of the uncertainty in your data; (c) your analysis including your identification of the focal lengths to high precision, your mathematical model for the relationship between focal length, object distance, and image distance, and your statistical evaluation of your model; and (d) an introduction and conclusion in which you summarize and evaluate your work, summarize what the results mean qualitatively (e.g. what do your results tell you about where a lens needs to be placed to achieve a focussed image or whether a given lens would even work), and propose improvements to your experimental methods. Everything should be supported by data. If you would like to include hand-drawn elements (such as ray-diagrams), please do so. 'Biologists often call this the "working distance" Adapted from Moore, Giannini, Nordstrom, and Losert (U. of Maryland, College Park)About the Equipment Each group will have access to the following: a a light source (your object} a a set of converging lenses (hiconvex) each with a di'erent focal length. a an optical bench and mounting apparatus for your lenses and light source a a meter stick and a ruler Be sure that your optical elements, such as lenses1 are carefully aligned with the axis of the optical bench. If you need help with this or are not sure why this is important, please ask your TA. Additionally, please be gentle with the equipment, mpecially the glass lenses, and try to avoid getting ngerprints, skin oils, or dirt on the lenses. Approximate timing: Week 1: 0 Introduction/ review of pro-lab .............. 10 min. a 1 u an. 1- Approximate timing: Week 1: Introduction/review of prolab .............. Analysis of ts .............................. Determine Focal Lengths .................... Design Experiment ......................... Gather Data ................................ Planning for next week ..................... Before Week 2: Between the end of this mk's lab and the start of next week's lab, you and your group should collabo ratively compile a rough draft of your formal reportwrite what you can, now, and plan out what data needs to be collected and what analyses need to he done next week. This will count towards your Week 1 grade (if you miss week 2). The Labor Contract can help you designate rmponsibilities. This draft is due at the beginning of the Week 2 lab. Week 2: '- Analyze Data and Create Model ............ 60 min. '- Finalize Report ............................. 50 min. Your nal lab should be ready submit at the end of your Week 2 lab; you are welcome to take a few extra hours to polish it up. but this is not meant to be additional out of clan-i work. Adapted from Moore, Giannini, Nordstrem, and Laser! (U. of Maryland, College Park} Din-um ll"): Donn '1 1 Recapping the prelab 1.1 Lenses and Focal Points 1. With your group, discuss the ideas of the image and the focal point. What are they? What is the difference between these concepts? Are they ever the same thing? If so, when? Are they always the same thing? STOP! Your instructor will lead a discussion of everyone's ideas 2. Summarize this discussion. 1.2 Analyzing fits Student A: y = 10x - 11 Student B: y = 11x - 21 1001.2 Analyzing fits Student A: y = 10x - 11 Student B: y = 11x - 21 100 stretch force uncertainty in force 60 measurement force [N] cm [N] [N] 1 Student C: y = 5x - 3 Student D: y=x3 + 6 00 00 00 H H H 100 60 force [N] 40 20 Table 1: Stretch and Force data extension [cm] extension [cm] Table 2: Four different fit lines for the same data. Adapted from Moore, Giannini, Nordstrom, and Losert (U. of Maryland, College Park)Phys 1125 Page 4 1. With your group, invent at least two ways to quantitatively evaluate the quality of a fit line to data. Your methods should allow you to compare which student's model is a better fit to the data with a single number such that a smaller value indicates a better fit. The goal is to be creative work with information to invent solutions to a problem. STOP! Your instructor will lead a discussion of everyone's ideas 2. Summarize this discussion. 3. Use the data and graphs to compute the quality of the fit for one student (assigned by your TA). This can be done through Excel or another spreadsheet program. Record these below.3' Use the data. and graphs to compute the quality of the lit for one student (assigned by your TA]. This can he done through Excel or another spreadsheet program. Record those below. Adapted from Manna, Giannini, Nmslrmn, and Lose (U. of Maryland, College Park)