Homework Help: Thin lens, optics

1. The problem statement, all variables and given/known data
Show that the minimum distance between 2 conjugate points (real object and image) for a positive thin lens is 4f.


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


3. 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?

 

Wow, this worked. Awsome! So I only needed the formula [tex]\frac{1}{f}=\frac{1}{S_o}+\frac{1}{S_i}[/tex] and your nice idea!

Edit: Wait! Why did you choose the expression So-Si rather than minimizing So+Si?

 

But this worked! ahahahaha, I made an error but I reached the result. Wow, amazing. I'll retry. Ahahahah.

 

Have you solved the problem? I'm getting stuck, I just don't reach anything. [tex]S_0+S_i=\frac{S_0S_i}{f}[/tex]. I have to minimize this function.

 

Worked! Thanks a lot.