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Question Number 165617 by mathls last updated on 05/Feb/22

what is the focal length formula for   combined lenses? if lenses more than   tow?

$${what}\:{is}\:{the}\:{focal}\:{length}\:{formula}\:{for}\: \\ $$$${combined}\:{lenses}?\:{if}\:{lenses}\:{more}\:{than}\: \\ $$$${tow}? \\ $$

Answered by aleks041103 last updated on 05/Feb/22

If you have two thin lenses with optical  power Φ_1  and Φ_2  placed a distance D appart  then the total optical power of the  system is Φ  Φ=Φ_1 +Φ_2 −DΦ_1 Φ_2

$${If}\:{you}\:{have}\:{two}\:\boldsymbol{{thin}}\:{lenses}\:{with}\:{optical} \\ $$$${power}\:\Phi_{\mathrm{1}} \:{and}\:\Phi_{\mathrm{2}} \:{placed}\:{a}\:{distance}\:{D}\:{appart} \\ $$$${then}\:{the}\:{total}\:{optical}\:{power}\:{of}\:{the} \\ $$$${system}\:{is}\:\Phi \\ $$$$\Phi=\Phi_{\mathrm{1}} +\Phi_{\mathrm{2}} −{D}\Phi_{\mathrm{1}} \Phi_{\mathrm{2}} \\ $$

Commented by aleks041103 last updated on 05/Feb/22

here Φ:=(1/f), where f is the focal length  measured in meters(positive if the  lens is comvex and negative if concave) and   Φ is the optical power measured in  dpt=m^(−1) .

$${here}\:\Phi:=\frac{\mathrm{1}}{{f}},\:{where}\:{f}\:{is}\:{the}\:{focal}\:{length} \\ $$$${measured}\:{in}\:{meters}\left({positive}\:{if}\:{the}\right. \\ $$$$\left.{lens}\:{is}\:{comvex}\:{and}\:{negative}\:{if}\:{concave}\right)\:{and}\: \\ $$$$\Phi\:{is}\:{the}\:{optical}\:{power}\:{measured}\:{in} \\ $$$${dpt}={m}^{−\mathrm{1}} . \\ $$

Commented by mathls last updated on 06/Feb/22

if lenses more than tow thin lenses?

$${if}\:{lenses}\:{more}\:{than}\:{tow}\:{thin}\:{lenses}? \\ $$

Commented by aleks041103 last updated on 06/Feb/22

I′m not sure. I′ll try using matrix optics.

$${I}'{m}\:{not}\:{sure}.\:{I}'{ll}\:{try}\:{using}\:{matrix}\:{optics}. \\ $$

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