How to determine a lens width?

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To determine lens width for focusing an image at 3 cm, the focal length is crucial, governed by the lens formula 1/f = 1/u + 1/v. The lens must be a convergent type, typically with a specific curvature affecting the angle of incidence. Simply placing an object directly on the lens is ineffective for forming a clear image at a finite distance. A small object distance, such as 1 mm, can still achieve focus at 3 cm if the focal length is appropriate. Understanding these principles is essential for effective lens design and application.
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I am wondering... say an object was put directly on a lens and you wanted the projected image to focus at around 3 cm on the other side. How do you determine how wide the lens has to be?
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"how wide" in itself is not enough to specify this, since the angle of incedence depends on the curvature of the lens. you must look for a lens wth the correct focal length, where
1/f = 1/u + 1/v (if I'm remembering correctly)

the top bit of this page explains...
http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/lenseq.html
 
Ah, so it is also determined by the shape. However, i expect it would need to be a convergent lens type and assume it needs to be like a () shaped lens. The problem is however, that this equation can help find focal length but not describe how the lens itself will be shaped.
 
Placing an object directly in contact with a lens (any lens) is not a good way to form an image any finite distance away from the lens. Why do you want to do this?
 
Simply curious if its possible. I'm not sure it is, which is why I'm wondering. What about if the object is a very small distance from the lens, like say 1 mm. Can you focus the image on the other side 3 cm away?
 
Sure, if the focal length of the lens is correct. That's how a microscope objective works.
 

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