Đáp án:

a) \(f = 6cm\)

b) \(f = 10cm\)

Giải thích các bước giải:

a) Ta có: 

\(\begin{array}{l}
\dfrac{{AB}}{{A'B'}} = \dfrac{{OA}}{{OA'}} \Rightarrow 4 = \dfrac{{30}}{{OA'}} \Rightarrow OA' = 7,5cm\\
\dfrac{{AB}}{{A'B'}} = \dfrac{{OI}}{{A'B'}} = \dfrac{{OF'}}{{OA' - OF'}} = \dfrac{f}{{7,5 - f}}\\
 \Rightarrow 4 = \dfrac{f}{{7,5 - f}} \Rightarrow f = 6cm
\end{array}\)

b) Ta có: 

\(\begin{array}{l}
\dfrac{{AB}}{{A'B'}} = \dfrac{{OA}}{{OA'}} \Rightarrow 4 = \dfrac{{30}}{{OA'}} \Rightarrow OA' = 7,5cm\\
\dfrac{{AB}}{{A'B'}} = \dfrac{{OI}}{{A'B'}} = \dfrac{{OF}}{{ - OA' + OF}} = \dfrac{f}{{f - 7,5}}\\
 \Rightarrow 4 = \dfrac{f}{{f - 7,5}} \Rightarrow f = 10cm
\end{array}\)