Graphically determining the focal length of a converging lens

AI Thread Summary
To determine the focal length of a converging lens graphically, plot the values of 1/di on the y-axis and 1/do on the x-axis. Rearranging the lens formula 1/f = 1/do + 1/di allows for the identification of a linear relationship, where the graph should yield a line with a slope of -1 and a y-intercept of approximately 1/f. Each data point corresponds to the ordered pairs (1/do, 1/di), which must be plotted accurately. The x-intercept of the graph will also provide the focal length, confirming its consistency as a constant value.
ilovemycat
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Homework Statement
Graphically determining the focal length of a converging lens by graphing the given object distances (do) and image distances (di)
Relevant Equations
1/f = 1/do + 1/di
So I have plotted all the given data points on a graph, putting 1/di on the y- axis and 1/do on the x-axis. I have to now find focal length from the graph? I'm not sure how, I'm thinking I have to rearrange the equation 1/f = 1/do + 1/di into y = mx + b form then go from there, but I'm totally unsure how to do this. Can anyone provide guidance? Thanks
 
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yes, i have not been asked to provide a ray diagram. heres the graph i made:
Screenshot 2023-11-05 at 8.20.42 PM.png

unsure how to find focal length just graphically...
 
There must be some kind of instructions that accompany these data whether they were provided to you or you collected them doing an experiment. What are these instructions?

It would also help if you provided a table of values instead of a graph. The graph you provided shows di as a function of do. What makes you think that is the right things to plot? Look at the "relevant equation" that you posted and think what you must plot to extract the focal length from the numbers you have. Remember that the focal length is a constant independent of di and do.
 
ilovemycat said:
Homework Statement: Graphically determining the focal length of a converging lens by graphing the given object distances (do) and image distances (di)
Relevant Equations: 1/f = 1/do + 1/di

So I have plotted all the given data points on a graph, putting 1/di on the y- axis and 1/do on the x-axis. I have to now find focal length from the graph? I'm not sure how, I'm thinking I have to rearrange the equation 1/f = 1/do + 1/di into y = mx + b form then go from there, but I'm totally unsure how to do this. Can anyone provide guidance? Thanks
It appears that you have been given set of object distances and image distances. It stands to reason that each image distance is paired with a particular object distance. From each pair ##\displaystyle \left \{ d_o\, ,\, d_i \right \} ## get the ordered pair ##\displaystyle \left ( 1/d_o\, ,\, 1/d_i \right ) ## and plot that as a pint on your graph.

Since each point has a ##y##-coordinate of ##\displaystyle 1/d_i ## , you should solve the equation ##\displaystyle 1/f = 1/d_o+1/d_i ## for ##\displaystyle 1/d_i ##. Comparing the resulting equation to the equation ##\displaystyle \quad y=mx+b## , your graph should have points lying roughly along a line with a slope of ##-1## having a y-intercept of about ##\displaystyle 1/f## .

Notice that the x-intercept is also ##\displaystyle 1/f## .
 
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