We know a/c to Gullstrand's equation that the effective focal length of two lenses separated by a distance $d$ is given as $$\frac{1}{f_{eq}}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1f_2},$$ but the equation doesn't clarify on the position of the lens having this effective focal length, how do i calculate that?
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2 Answers
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If you were to switch the two lenses by a single thin lens, then the answer is tricky, because you can't just literally remove the two lenses from your optical table and put somewhere a lens of effective focal length expecting everything else would be the same.
What you can do is make an equivalent lens system: a box containing the effective lens at a given distance from the front $d_f$ and the back $d_b$ of the box. The length of this box is in general $d_f + d_b \neq d$, and so, when you replace your two lenses by this box, you would have to move all the optics you had after the pair of lenses. Note that if the two lenses are near a telescope arrangement, then this equivalent box would have near infinity length.
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Well, the distance will simply be the EFL - i.e. given the position of the final spot/image the lens will be at the EFL distance.
