`h=0,4mm=0,0004cm`

`h'=4mm=0,04cm`

`G=25/f=>f=25/G=25/10=2,5cm`

Lập tỉ lệ:

`h/{h'}={0,0004}/{0,04}=1/10`

Xét `\triangleOAB` $\backsim$ `\triangleOA'B'`. Ta có:

`{OA}/{OA'}={AB}/{A'B'}=1/10`          `(1)`

Xét `\triangleOIF'` $\backsim$ `\triangleA'B'F'`. Ta có:

`{OF'}/{A'F'}={OI}/{A'B'}`          

Mà OI=AB

`=>` `{OF'}/{A'F'}={AB}/{A'B'}`          `(2)`

`(1)(2).` Ta có:

`{OA}/{OA'}={OF'}/{A'F'}`

`=>` `1/10={OF'}/{A'F'}`

`=>` `OA'-2,5=2,5OA'`

`=>` `OA'=27,5cm`

Thay vào (1)

`=>` `OA={2,75}/10=2,75cm`

Đáp án:

 \(2,75cm\)

Giải thích các bước giải:

Ta có: 

\(f = \dfrac{{25}}{G} = \dfrac{{25}}{{10}} = 2,5\left( {cm} \right)\)

\(\begin{array}{l}
\dfrac{{AB}}{{A'B'}} = \dfrac{{OA}}{{OA'}} = \dfrac{{0,4}}{4} = \dfrac{1}{{10}}\\
\dfrac{{AB}}{{A'B'}} = \dfrac{{OI}}{{A'B'}} = \dfrac{{OF'}}{{OA' - OF'}} = \dfrac{{2,5}}{{OA' - 2,5}}\\
 \Rightarrow \dfrac{1}{{10}} = \dfrac{{2,5}}{{OA' - 2,5}} \Rightarrow OA' = 27,5cm\\
 \Rightarrow OA = 2,75cm
\end{array}\)