- #1

fluidistic

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## Homework Statement

Show that the minimum distance between 2 conjugate points (real object and image) for a positive thin lens is 4f.

## Homework Equations

[tex]\frac{1}{f}=\frac{1}{S_o}+\frac{1}{S_i}[/tex].

## The Attempt at a Solution

I assumed the lens to be biconvex (though I know that I can't. There are so many types of positive lens...).

So I get that [tex]\frac{1}{f}=(n_1-n_0)\left ( \frac{2}{R} \right )[/tex].

So I must show that [tex]S_0+S_1 \geq 4f[/tex].

Using these 2 formulae, I reach that the inequation holds if and only if [tex]S_0+S_i \leq 2R[/tex] where R is the curvature radius of the thin lens. I'm stuck here. Are there any other equation I should use? Or am I in the right direction?