WELCOME TO THE INTERACTIVE PHYSICS TUTORIAL…

1. WELCOME TO THE INTERACTIVE PHYSICS TUTORIAL… This is a presentation that works much like a slide show. To Proceed through the slides all you have to do is click on the left mouse button. Try to click only once at a time. To go backwards just click the right mouse button and choose the option ‘previous.’

2. Give an appropriate title to show the relationship being plotted. Graphing sample Label both the x and y axis. Include the variable name, symbol, and unit of measurement. WAVELENGTH l (m) In Setting up your graph, choose an appropriate scale. INVERSE FREQUENCY n-1(10-2s)

3. Graphing sample The graph paper will usually have divisions in tenths (e.g. One centimetre blocks subdivided into millimetres), so do not make a scale that divides these into an inconvenient fraction like thirds or sixths. Instead, choose a scale that divides the scale into groups of 2, 4, or 5. The scale you will choose will depend upon the range of data you are plotting. Choose a scale so that:  your graph uses as much graph paper as possible, and  your scale has a convenient number of divisions. Here’s a way to pick a scale: 1) Count how many gridblocks are available on the graph paper. Remember to use the full page 2) Divide the range of data you are plotting by the number of available gridblocks. If the answer comes out to a nice value, you can proceed with the plot. If the value is awkward, choose a different number of gridblocks. Here’s an example: There are 23 gridblocks available to plot data in the range of o to 1. Doing the calculation gives: 1/23 = .0434 units per gridblock, which is horrible to work with. If you choose 20 gridblocks, then you will get: 1/20 = .05 units per gridblock, which is reasonable. This scale will use most of the available page, and divides the gridblocks into fractions that are easy to work with since each centimetre block is .05 units, and each millimetre block is .005 units.

4. Graphing sample Plot the points from your data. WAVELENGTH l (m) INVERSE FREQUENCY n-1(10-2s)

5. Graphing sample For each point on the graph, draw error bars. (Bars are not drawn to scale here for clarity) These bars are just the reading errors drawn on the graph. Draw the bars to scale with the +/- values indicated in the lab result table. Bars are drawn on both sides of each point for it’s ‘y’ and ‘x’ coordinates. It is important to note that the point itself is most likely to be the true measure, while areas along the bars are less likely to be true measures. WAVELENGTH l (m) INVERSE FREQUENCY n-1(10-2s)

6. Graph Sample As you move from the point, along the error bar (both ‘x’ and ‘y’) the colour becomes lighter representing that values, as they move away become less and less likely to be the true measures. Perhaps the easiest way to represent this concept is through a colour gradient. Picture the darkest red area (the plotted point) as the closest value to the true measure.

7. Graphing sample The next step is to drawa Best Fit Line of the points. Use your judgement to find the best placement. Opposite that of the Maximum Slope Line, a Minimum Slope Line is drawn by making a straight line between the end of the right side error bar on the highest point and extending a line down to the end of leftside error bar on the lowest point. WAVELENGTH l (m) After you have plotted the error bars on each point, draw the Maximum Slope Line. Start at the at the end of the leftside error bar on the highest point plotted and extending a line down to the end of the rightside error bar on the lowest point plotted. INVERSE FREQUENCY n-1(10-2s)

8. Graphing sample After you draw all the lines, label them, and calculate their slopes. (.8,1.015) Maximum Slope Line To calculate the slope try to pick two points that are convenient to use. (Do not pick points that have already been plotted.) For an example let’s choose to find the slope of the Maximum Slope Line: WAVELENGTH l (m) Best Fit Line Minimum Slope Line The first coordinate could be (.1,.065) and the second, (.8,1.015) (The plots chosen would have been read off a proper graph with much finer gridlines.) (.1,.065) INVERSE FREQUENCY n-1(10-2s)

9. Graphing sample (.8,1.015) The slope is calculated by the rise over the run: (y2-y1)/(x2-x1) = (1.015-.065)/(.8-.1) x 10-2 = 1.36 x 102 ms-1 Maximum Slope Line WAVELENGTH l (m) Calculate the slope in the same way for each line. Using the same points for calculating each slope may make the process easier. Don’t forget to use scientific notation, and to place the proper unit of measurement after your final value. (.1,.065) INVERSE FREQUENCY n-1(10-2s)

10. Graphing sample This scale is inappropriate as well. You should try to use up as much graph surface as possible. The graph here is far too cramped at the bottom This is an example of a poorly plotted graph. See if you can find all the problems with it before proceding Here the y-axis variable isn’t even labelled The size of these points are too large and such inprecision can cause inaccurate calculation results. A scale like this make the graph hard to read and interpret First of all, the title says nothing about the variable relationship being displayed This label fails to provide the variable symbol and unit of measurement The maximum and minimum slope lines are not labelled here Best Fit Line The line of best fit here is out of place. This line should not extend beyond the range of the maximum slope line and minimum slope line. It should try to strike midway between the plotted points within the range. INVERSE FREQUENCY There should also be gridlines present. All graphs should be drawn on standard graphing sheets

11. Graphing sample Once again, this is what the proper graph should look like when completed. Maximum Slope Line For sake of simplicity, not all points contain horizontal and vertical error bars. Your graph should have them plotted. WAVELENGTH l (m) Best Fit Line Minimum Slope Line INVERSE FREQUENCY n-1(10-2s)

12. You have completed the graphing tutorial. To return to the main lab site click here. Presentation created by: Craig Fraser