Focal length of converging thin lens graphs

[jribs]

Homework Statement

So in my physics assignment we had to graph the negative of magnification (-M) versus distance between image and lens (q). From this we had to find the focal lengths from the intercepts. I have the focal length using the x intercept of the equation M=1-q/f (which I rearragened to -M= q/f -1) but I can’t figure out how to find the focal length using the y intercept.

Relevant Equations

Y=mx+b is equivalent to -M=1/f•q -1
Focal point using x intercept: x0=-b/m=f

I tried -M=pq = f/(f-p) = f/f - f/p = 1-(f/p)
=> M+1= -f/p
=> -Mp-p=f

But since it’s the y intercept, p will equal zero and so the focal length will be 0?

 

[kuruman]

I tried -M=pq = f/(f-p) = f/f - f/p = 1-(f/p)
=> M+1= -f/p
=> -Mp-p=f

But since it’s the y intercept, p will equal zero and so the focal length will be 0?

If your task is to graph the negative of the magnification -M versus the distance of the image from the lens q, what is p doing in your equations? Starting from the thin lens equation and the magnification equation, eliminate the object distance p to get an equation between M and q. Then substitute y for (-M) and x for q and see if you can bring the result to the form y = a x + b.