For a spherical mirror under the paraxial approximation, the focal length $f$ and radius of curvature $R$ are related by 
A$f=R$
B$f=2R$
C$f=R/2$
D$f=R/4$
Answer & Solution
Correct answer: C. $f=R/2$
Using the geometry of reflection for paraxial rays and the small-angle approximation, one obtains $\mathrm{FD}=\mathrm{CD}/2$. Since for paraxial rays $\mathrm{FD}=f$ and $\mathrm{CD}=R$, it follows that $f=R/2$.
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