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Ray Optics and Optical Instruments
Refraction at Lenses – Lens Maker's Formula and Combination
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- equivalent focal length of a lens combination
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2023 1 question
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In the figure shown here, what is the equivalent focal length of the combination of lenses (Assume that all layers are thin)?
Using $\frac{1}{f}=(\mu-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$ for each layer and adding: $f_{net}=-100\ cm$.
$\frac{1}{f_1}=(1.6-1)\left(\frac{1}{\infty}-\frac{1}{20}\right)=-\frac{3}{100}$ $\frac{1}{f_2}=(1.5-1)\left(\frac{1}{20}-\frac{1}{-20}\right)=\frac{1}{20}$ $\frac{1}{f_3}=\frac{1}{f_1}=-\frac{3}{100}$ $\frac{1}{f_{net}}=\frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3}=-\frac{3}{50}+\frac{1}{20}$ $\Rightarrow f_{net}=-100\ cm$