Stargazing Problem about calculating focal length of a telescope

AI Thread Summary
The discussion revolves around a formula for calculating the focal length of a telescope, specifically focusing on a step in the derivation that involves the term -(1+b). The user seeks clarification on how this term is obtained from the previous equation, expressing confusion over a sign discrepancy in the second term. They understand the substitutions made but request a detailed walkthrough of the mathematical steps involved. The conversation highlights the importance of precise mathematical manipulation in optics. Overall, the thread emphasizes the need for clear explanations in complex formula derivations.
Blacky&Imy
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Hello!
I am preparing an exam about optics and I can't understand a formula.my problem is at the end of the second page (the explanation is in Italian, but the formulas are easy to read for everybody).
I can't understand how in the last step

f=R/2 - (1+b) * r^2/4R etc they found -(1+b)

can somebody help me please?
 

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Are you asking how they mathematically got from the previous equation to the last one?
 
yes. I understand what is substituted in what, but I get a different sign in the second term, and I'd like to see all the passages...
 

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