# Finding the focal length of a negative lens without another lens.

#### kPepis

1. Homework Statement
A simple method for determining the focal length of a negative lens is shown below. Prove this is true.

2. Homework Equations

3. The Attempt at a Solution
The linear magnification formula relates magnification, the distance from the lens to the image (i), the distance from the lens to the object (o) and the height of the two images (h'/h). The lens equation relates distance to the object and distance to the image and the focal length. I know I have to use these two equations but I have not been able to prove this is true. This is kind of frustating considering it's a simple problem, but can anyone point me in the right direction?

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#### nasu

I don't think you have to use the formulas above. What you have on the screen is not the image of any object.
What kind of image will be produced by a divergent lens? Can you catch on a screen? Where will be the image of the sun produced by the lens?

But the problem it is much simpler. Is pure geometry. If you extend the divergent rays (the ones on the left hand side of the lens) to the right hand side of the lens, they will meet in a point. What is the location of this point? How far from the lens?

"Finding the focal length of a negative lens without another lens."

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