Đáp án:
3 hoặc \(\dfrac{3}{7}\)
Giải thích các bước giải:
TH1: Thấu kính hôi tụ
Ta có:
\(\begin{array}{l}
\dfrac{{AB}}{{A'B'}} = \dfrac{{OA}}{{OA'}} = \dfrac{{16}}{{OA'}}\\
\dfrac{{AB}}{{A'B'}} = \dfrac{{OI}}{{A'B'}} = \dfrac{{OF'}}{{OA' - OF'}} = \dfrac{{12}}{{OA' - 12}}\\
\Rightarrow \dfrac{{16}}{{OA'}} = \dfrac{{12}}{{OA' - 12}} \Rightarrow OA' = 48cm\\
\Rightarrow \dfrac{{A'B'}}{{AB}} = 3
\end{array}\)
TH2: Thấu kính phân kỳ
Ta có:
\(\begin{array}{l}
\dfrac{{AB}}{{A'B'}} = \dfrac{{OA}}{{OA'}} = \dfrac{{16}}{{OA'}}\\
\dfrac{{AB}}{{A'B'}} = \dfrac{{OI}}{{A'B'}} = \dfrac{{OF}}{{ - OA' + OF}} = \dfrac{{12}}{{12 - OA'}}\\
\Rightarrow \dfrac{{16}}{{OA'}} = \dfrac{{12}}{{12 - OA'}} \Rightarrow OA' = \dfrac{{48}}{7}cm\\
\Rightarrow \dfrac{{A'B'}}{{AB}} = \dfrac{3}{7}
\end{array}\)