What is the minimum image-object distance in a single lens system?

[kehler]

Homework Statement

For a system with a single lens, what is the smallest image to object distance that you can achieve?

Homework Equations

I guess (1/f)=(1/i)+(1/o)

The Attempt at a Solution

Tried drawing a few ray diagrams but didn't seem to get anywhere :S

 

[mal4mac]

Here's a clue:

"...a simple microscope, which consists of a single convex lens. Magnification is given by the ratio of the image distance, the distance between the lens and the image, and the object distance, the distance between the lens and the specimen. As the object distance decreases, the size of the magnified image increases proportionally. When the object distance reaches the focal plane of the lens, however, the rays exiting the lens emerge parallel, and no real image is created. In order to create a real image, the object distance must be greater than the focal length of the lens. A shorter focal length allows for a shorter distance between the object and the lens, and enables greater magnification."

http://laser.physics.sunysb.edu/~scott/liquid-lens/

 

[kehler]

Hm thanks. I guess that tells me it has to be greater than f, so the distance must be greater than 2f...
Is there any way to do it by differentiation? Cos that's how minimum values are usually found, right? I would try differentiating (1/f)=(1/i)+(1/o) but I don't know what I'm differentiating with respect to :S

 

[mgb_phys]

You would write an equation for the total length ie, s=o+i in terms of 'o' or 'i' and f
I think you have to make the assumption that the system is symetric and so i=o.