Guide to Lab Reports and Lab Grading A. Introduction The purpose of a lab report is to communicate results of observations which test a theoretical prediction, and enable others to repeat the observations using the same conditions. Theory or prior experiments tell us what we expect (e.g., what is predicted or known ), whereas measurement tells us what we get. We compare the two using uncertainty and error to see if the theory is verified or not. In particular, if the error is less than the experimental uncertainty, the prediction is verified ; otherwise, it is not verified. Scientific experiment is all about reproducibility one must be able to repeat an experiment and get the same results within a certain range of uncertainty if the experiment is to have value. The lab report should be written from the point of view of a reader who is unfamiliar with the experiment, but who can perform the experiment again under identical conditions as described in the report. B. Format In this course we require a specific format (see figure on the next page). It basically consists of the following four sections: I. Introduction II. Data and Analysis III. Summary and Conclusions The Introduction summarizes the purpose, expectation (theory), and procedure used for observation. It should be sufficient to enable another person to repeat the experiment. A picture of the apparatus is almost always helpful. The procedure of the lab should be made very clear, as should the theory used to analyze and predict results. The Data and Analysis section contains all the measurements and calculations in tables and graphs. Tables should include each observation made. Units must be included where appropriate. Significant figures are critical. The average of a list of values should be included, as well as uncertainty (and error if a known value is available). The calculation of uncertainty and error must be discussed. Also, any graphs and curve fitting should be placed here. Graphs should include data points as individual bullets, circles, points, etc., and where appropriate, theoretical curves on the same graph as the data. Summary and Conclusions should state the key results. This includes whether the observations verify the theoretical prediction or not. This is done by comparing the error and uncertainty; if the error < uncertainty the theory is verified, otherwise it is not verified. A sample report is in the Appendix. Helpful detail is also contained in the following links: http://lpc1.clpccd.cc.ca.us/lpc/physics/pdf/labwrtbg.pdf and http://abacus.bates.edu/~ganderso/biology/resources/writing/htwtoc.html. The following is a summary of the format: 1
Title I. Introduction Write a sentence or two describing the purpose (e.g., to explore the nature of uncertainties and error in measuring density ). Include one or more paragraphs summarizing what is expected, i.e., include theory here, derivations, key theoretical formulas. Number the equations or formulas for reference in the data and analysis section. Then, describe the experimental set up (a picture is helpful) and procedure. This description should enable someone to repeat what you did, so materials and apparatus description is important. Do not just copy procedure from the lab handout! Say what you or your team did. Takes 1-3 pages depending on the complexity of theory or procedure. II. Data and Analysis Put data in tables example: Table 1. Measurements of the Cylinder Tool Length (cm) Width (cm) Mass (g) Density (g/cm 3 ) ruler 1.26 0.96 8.208 9.0 caliper 1.2593 0.9577 9.045 Make a heading on top (see Table 1). A reference to it must appear in the text. Don t forget units. Take care of significant figures. State all uncertainties not taken into account by significant figures alone (e.g., 1.25 ± 0.06 cm, or include uncertainty as a separate column). Describe the analysis. How did you calculate quantities uncertainty, error, etc.? Use theoretical formulas for calculations. State mean values from the average of a data set, or maybe from a fit to a graph (if so, show the graph). Show sample calculations of uncertainties and errors. Show all graphs here, and text must refer to them. Clearly label axes. Data should clearly show data points and uncertainties as error bars. If theory is available, represent it as a continuous curve (possibly achieved with a best fit analysis). Takes 2-4 pages, depending upon the complexity of analysis. III. Summary and Conclusions State key measurements. Compare the error to uncertainty and state verified or not verified. Account for not verified results. Answer any specific questions posed in the lab handout. Takes a ½ to 1 page. 2
C. Some simple guidelines for calculating half-ranges Uncertainty for composite quantities (like density = m/v) Uncertainty = [(high val)-(low val)]/2 High val = high numerator/low denom Low val = low numerator/high denom High/low num or denom mean plus/minus uncertainty of composite variable Extracting uncertainties from graphs whose data points have uncertainty. Horizontal asymptote Last value with its uncertainty, or fit to appropriate curve Linear graph Slope, uncertainty determined by slope+ and slope-, e.g: (last+unc)-(first-unc) D. Helpful features of MS-Word subscripts/superscripts : CTRL-ALT-(SHIFT)-+ or CTRL-ALT- = Symbols: Insert Symbol and scroll to desired row, select item and press insert E. Grading deductions (out of 10.0 max score) Here is a list of the most common errors and point deductions used in grading the lab report: reason deduction missing section 1.0 results way too far off what is expected 0.5 1.0 missing error 0.50 missing uncertainty 0.50 missing comparison of error and uncertainty to verify or not verify 0.50 incorrect number of significant figures 0.25-0.50 incomplete or incorrect explanation or conclusion 0.25-0.50 inconsistency in results among various sections (e.g., stating one value in 0.25-0.50 one place, and another value in another place for the same measurement) missing table column heading or table description/title 0.25 missing units 0.25 missing labels on a graphical axis 0.25 missing table or figure reference from text 0.25 3
Appendix: Sample Lab Report: (adapted from Project Caliper, Ted Walker, DVC) I. Introduction Building a Simple Telescope with Lenses in Combination In this laboratory exercise we wanted to observe how lenses could be used to create images and how lenses in combination could be used to make telescopes. We measured the focal lengths of two converging lenses using two different methods. We then constructed two telescopes and measured the magnification of each telescope experimentally, and compared these values to the theoretically expected magnifications. We wanted to measure the focal lengths of the two converging lenses using sun light. We took the two converging lenses outside and used each one to focus the sun s light rays to a point. The distance from the lens to the focused sunlight is defined to be the focal length f of the lens. We measured this distance for each lens using a meter stick, obtaining the first measurement of the focal lengths. We wanted to measure the focal lengths of the two converging lenses using another method to check our work. We set up an optical system in a dark room consisting of a light source object, one of the lenses and a small projection screen (see Figure 1, below). p q object lens screen Figure 1: Optical system to measure f We moved the components back and forth until a sharp inverted image of the object was projected on the screen. We then measured the distance from the light object to the lens (p) and from the lens to the projection screen (q). From the measurements of p and q we were able to calculate the focal length, f obtained from 1 1 1 + = (1) p q f We used this procedure to determine a second measure of the focal length for each of the converging lenses. We then set out to make a telescope. Theory tells us that two lenses held the sum of their focal lengths apart should form a telescope (see Figure 2). We simply held the converging lens with the smaller focal length close to one eye and the other lens the sum of their focal lengths further out from the first lens. We then measured magnification m for this telescope. To do this we looked at a series of chalk lines on the blackboard from across the room with the telescope. The lines were drawn every 10cm. We looked at the lines through the telescope with one eye and simultaneously looked at the same lines 4
with the other eye. What we saw was one set of lines magnified by the telescope superimposed over the same lines unmagnified as seen by the other eye. Since the method used to measure m is so subjective, each partner in our lab group measured m and we averaged the three numbers. f o + f e eye lens objective lens Figure 2: Telescope schematic. f o and f e are the focal lengths of the objective and eyepiece lenses, respectively. We then made another telescope using the diverging lens as the eye lens. We again determined the magnification of this telescope by looking at the lines on the chalk board. We noticed that this second telescope had the advantage of not inverting the image. The measurements are compared to the theory m= f / f (2) where f o and f e are the focal lengths of the objective and eyepiece lenses, respectively. II. Data and Analysis o Table 1-2 contain the focal length data. The uncertainties are based on the thickness of the lens, as well as the uncertainty in determining exactly when the sunlight was perfectly focused. The 5mm uncertainties in Table 2 are determined as follows: 1mm for the meter stick, 1mm for the lens thickness, 1mm for the position of the object and 2mm for determination of the best possible focus. Table 1. Focal lengths determined using sun light Lens focal length (cm) Lens 1 10.2 +/- 0.4 Lens 2 19.7 +/- 0.4 Table 2. Focal lengths determined using images Lens p(cm) q(cm) f(cm) = pq/(p+q) Lens 1 27.2 +/- 0.5 14.4 +/- 0.5 9.4 +/- 0.8 Lens 2 32.4 +/- 0.5 61.3 +/- 0.5 21.2 +/- 0.7 Telescope 1 was constructed using lens 1 as the eye lens and lens 2 as the objective. Telescope 2 was constructed using a 2.5cm focal length lens as the eye lens and lens 1 as the objective lens. We can calculate the expected theoretical magnifications using equation (2) (see Table 3). Since we trust the focal lengths determined with the sun light the most, we chose to use those numbers to calculate the expected magnifications. e 5
Table 3. Theoretical magnifications f (cm) o f (cm) e m = -f /f o e Telescope 1 19.7 10.2-1.93 Telescope 2 10.2-2.5 +4.08 The Table 3 values of m represent the known values which can be compared to measured magnifications (Table 4). The + refers to upright images while the refers to inverted images. Uncertainties are calculated using the half-range. Error is computed using the theoretical values from Table 3. Table 4. Measured magnifications Ted s m Annie s m Joe s m Average m uncertainty error Telescope 1-2.1-1.6-1.8-1.8 0.3-0.13 Telescope 2 +3.6 +4.2 +3.8 +3.9 0.2 + 0.18 This shows that errors are within uncertainty, verifying the predictions of equations (1) and (2). The two calculations of focal lengths are shown in Table 5. In the case of lens 1, the difference between the measured focal lengths was less than the sum of their uncertainties. This means that the Table 5. Summary of focal lengths calculated the two different ways f(cm) with sun light f(cm) with object Difference (cm) Lens 1 10.2 +/- 0.4 9.4 +/- 0.8 0.6 +/- 1.2 Lens 2 19.7 +/- 0.4 21.2 +/- 0.7 1.5 +/- 1.1 measured focal lengths were consistent with each other. Unfortunately, In the case of lens 2, the measured focal lengths were different by a little more than the uncertainties. This probably means that we underestimated the uncertainties. The most likely cause was not having the image in clear focus. This would mean that p and q for the second method weren t actually measured correctly. We probably needed more than 2mm uncertainty due to obtaining the best possible focus. The telescope magnifications measured were both about 5% lower than the magnifications predicted by theory. This is reasonable since the theoretical equation assumed that the object was very far away (our object was only about 15 feet away) and that the eye was relaxed (something that s hard to control). III. Summary and Conclusions In this lab we measured the focal lengths of two converging lenses using two methods: sunlight focusing on a point and an object s relative size upon magnification. The results were close, Lens1 being within uncertainty of the theoretical prediction, Lens2 about 40% outside the uncertainty (as stated above, is probably due to poor determination of what is focused in the object measurement). Measurement confirms theoretical predictions of magnification, as the error < uncertainty for both Telescopes. We then built two telescopes and determined their magnifications both experimentally and theoretically, getting consistent results within uncertainty. 6