# Graphically determining the focal length of a converging lens

• ilovemycat
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

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

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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## What is the principle behind determining the focal length of a converging lens graphically?

The principle involves using the lens formula and ray diagrams. By tracing the paths of light rays that pass through the lens, one can determine where the rays converge to form an image. The distance between the lens and the point where the rays converge is the focal length.

## What materials are needed to graphically determine the focal length of a converging lens?

To graphically determine the focal length, you typically need a converging lens, a light source (like a distant object or a collimated light beam), a screen to capture the image, a ruler or measuring tape, and a piece of graph paper or a whiteboard for drawing the ray diagrams.

## How do you set up the experiment to graphically determine the focal length?

Set up the lens on a holder and place the light source at a known distance from the lens. Position the screen on the other side of the lens to capture the image. Adjust the screen until a sharp image is formed. Measure the distance between the lens and the screen; this distance is the image distance. Use these measurements to draw a ray diagram and determine the focal length.

## How do you draw the ray diagram to find the focal length?

Start by drawing the principal axis and the lens at the center. Draw at least two rays from the top of the object: one parallel to the principal axis that refracts through the focal point on the other side, and one passing through the center of the lens that continues in a straight line. The point where these rays converge on the other side of the lens is the image point. Measure the distance from the lens to this point to find the focal length.

## What are common sources of error in graphically determining the focal length of a converging lens?

Common sources of error include inaccuracies in measuring distances, misalignment of the lens and light source, and errors in drawing the ray diagrams. Additionally, lens imperfections and external light interference can affect the sharpness of the image, leading to measurement errors.

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