Đáp án:

1. 2cm và 4cm

2. 4/3cm và 1,5cm

Giải thích các bước giải:

1. Thấu kính hội tụ:

* d = 40cm: Ảnh thật

Ta có: 

\(\begin{array}{l}
\dfrac{{AB}}{{A'B'}} = \dfrac{{OA}}{{OA'}} = \dfrac{{40}}{{OA'}}\\
\dfrac{{AB}}{{A'B'}} = \dfrac{{OI}}{{A'B'}} = \dfrac{{OF'}}{{OA' - OF'}} = \dfrac{{20}}{{OA' - 20}}\\
 \Rightarrow \dfrac{{40}}{{OA'}} = \dfrac{{20}}{{OA' - 20}} \Rightarrow OA' = 40cm\\
 \Rightarrow A'B' = 2cm
\end{array}\)

* d = 10cm: Ảnh ảo

Ta có:

\(\begin{array}{l}
\dfrac{{AB}}{{A'B'}} = \dfrac{{OA}}{{OA'}} = \dfrac{{10}}{{OA'}}\\
\dfrac{{AB}}{{A'B'}} = \dfrac{{OI}}{{A'B'}} = \dfrac{{OF'}}{{OA' + OF'}} = \dfrac{{20}}{{OA' + 20}}\\
 \Rightarrow \dfrac{{10}}{{OA'}} = \dfrac{{20}}{{OA' + 20}} \Rightarrow OA' = 20cm\\
 \Rightarrow A'B' = 4cm
\end{array}\)

2. Thấu kính phân kỳ:

* d = 40cm: Ảnh ảo

Ta có:

\(\begin{array}{l}
\dfrac{{AB}}{{A'B'}} = \dfrac{{OA}}{{OA'}} = \dfrac{{40}}{{OA'}}\\
\dfrac{{AB}}{{A'B'}} = \dfrac{{OI}}{{A'B'}} = \dfrac{{OF}}{{ - OA' + OF}} = \dfrac{{20}}{{20 - OA'}}\\
 \Rightarrow \dfrac{{40}}{{OA'}} = \dfrac{{20}}{{20 - OA'}} \Rightarrow OA' = \dfrac{{40}}{3}cm\\
 \Rightarrow A'B' = \dfrac{2}{3}cm
\end{array}\)

* d = 10cm: Ảnh ảo

Ta có:

\(\begin{array}{l}
\dfrac{{AB}}{{A'B'}} = \dfrac{{OA}}{{OA'}} = \dfrac{{10}}{{OA'}}\\
\dfrac{{AB}}{{A'B'}} = \dfrac{{OI}}{{A'B'}} = \dfrac{{OF}}{{ - OA' + OF}} = \dfrac{{20}}{{20 - OA'}}\\
 \Rightarrow \dfrac{{10}}{{OA'}} = \dfrac{{20}}{{20 - OA'}} \Rightarrow OA' = \dfrac{{20}}{3}cm\\
 \Rightarrow A'B' = 1,5cm
\end{array}\)