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Two thin convex lenses of focal length \mathrm{20\ cm} and \mathrm{25\ cm} are placed at a finite distance apart. The power of the combination is \mathrm{8\ D}. Distance between the lenses is:

Option: 1

\mathrm{5\ cm}


Option: 2

\mathrm{10\ cm}


Option: 3

\mathrm{8\ cm}


Option: 4

\mathrm{4\ cm}


Answers (1)

best_answer

\mathrm{\text { Here, } \mathrm{f}_1=20 \mathrm{~cm}, \mathrm{f}_2=25 \mathrm{~cm}, \mathrm{p}=8 \mathrm{D}}
Focal length of combination \mathrm{=\frac{1}{8} \mathrm{~m}=\frac{100}{8} \mathrm{~cm}}
Now, using \mathrm{\frac{1}{\mathrm{~F}}=\frac{1}{\mathrm{f}_1}+\frac{1}{\mathrm{f}_2}-\frac{\mathrm{d}}{\mathrm{f}_1 \mathrm{f}_2},} (where d is the distance between lenses), we get
\mathrm{\begin{aligned} & \frac{8}{100}=\frac{1}{20}+\frac{1}{25}-\frac{d}{20 \times 25} \\ & \Rightarrow \frac{d}{500}=\frac{1}{20}+\frac{1}{25}-\frac{8}{100}=\frac{5+4-8}{100}=\frac{1}{100} \\ & \text { or } \quad \mathrm{d}=\frac{500}{100}=5 \mathrm{~cm} \end{aligned}}

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