Real Images and Thin Lenses: Can You Explain the Postulation?

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Gear300
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I was reading a bit on thin lenses when a postulation was made that the image formed from the first surface would be the object for the second. The postulation made sense for when the first image is virtual, but I don't see how it works when the first image is real? Can anyone provide me the proper proof for this?
 
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what about cases with thick lenses?
 
You can model a thick lens by tracing the ray across the first surface through the body of the lens and across the second surface. YOu might have to do this for very thick lenses or odd setups. You can model combinations of thick lenses in a similair way to thin lenses - you just have to have a slightly different definition of the lens's position - eg nodal points.
 
I see...makes more sense now