Đáp án:
d1=97,3cm
Giải thích các bước giải:
\(AB = 2cm;{d_2} = {d_1} - 45cm;{A_2}{B_2} = 20cm;{d_2} - {d_1} = 18cm\)
Ta có:
\(\dfrac{{{A_2}{B_2}}}{{AB}} = \dfrac{{{d_2}'}}{{{d_2}}} \Leftrightarrow \dfrac{{20}}{2} = \dfrac{{18 + {d_1}'}}{{{d_1} - 45}} \Leftrightarrow 20{d_1} - 900 = 36 + 2{d_1}' \Leftrightarrow {d_1}' = 10{d_1} - 936\)
Tiêu cự:
\(\dfrac{1}{f} = \dfrac{1}{{{d_1}}} + \dfrac{1}{{{d_1}'}} = \dfrac{1}{{{d_2}}} + \dfrac{1}{{{d_2}'}} \Leftrightarrow \dfrac{1}{{{d_1}}} + \dfrac{1}{{10{d_1} - 936}} = \dfrac{1}{{{d_1} - 45}} + \dfrac{1}{{10{d_1} - 936 + 18}} \Rightarrow {d_1} = 97,3cm\)