Problem about calculating focal length of a telescope

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SUMMARY

The forum discussion centers on the calculation of the focal length of a telescope using the formula f=R/2 - (1+b) * r^2/4R. The user seeks clarification on how the term -(1+b) is derived in the final equation. Participants confirm that the issue lies in the mathematical manipulation of the equation, specifically in the sign of the second term. Detailed steps are requested to elucidate the transition from the previous equation to the final form.

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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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