Graphically determining the focal length of a converging lens

[ilovemycat]

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

 

[kuruman]

Please post the statement of the problem as given to you. Are you sure you are not asked to produce a ray diagram? Also, post what you have tried so far.

Please read, understand and follow our homework guidelines, especially item 4, here
https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

 

[ilovemycat]

yes, i have not been asked to provide a ray diagram. heres the graph i made:

unsure how to find focal length just graphically...

 

[kuruman]

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.

 

[SammyS]

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 $\displaystyle 1/f$ .