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


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

$w h a t i s t h e f o c a l l e n g t h f o r m u l a f o r$ $c o m b i n e d l e n s e s ? i f l e n s e s m o r e t h a n$ $t o w ?$
	Answered by aleks041103 last updated on 05/Feb/22

	$I f y o u h a v e t w o t h i n l e n s e s w i t h o p t i c a l$ $p o w e r Φ_{1} a n d Φ_{2} p l a c e d a d i s t a n c e D a p p a r t$ $t h e n t h e t o t a l o p t i c a l p o w e r o f t h e$ $s y s t e m i s Φ$ $Φ = Φ_{1} + Φ_{2} - D Φ_{1} Φ_{2}$
	Commented by aleks041103 last updated on 05/Feb/22

	$h e r e Φ := \frac{1}{f}, w h e r e f i s t h e f o c a l l e n g t h$ $m e a s u r e d i n m e t e r s (p o s i t i v e i f t h e$ $l e n s i s c o m v e x a n d n e g a t i v e i f c o n c a v e) a n d$ $Φ i s t h e o p t i c a l p o w e r m e a s u r e d i n$ $d p t = m^{- 1} .$
	Commented by mathls last updated on 06/Feb/22

	$i f l e n s e s m o r e t h a n t o w t h i n l e n s e s ?$
	Commented by aleks041103 last updated on 06/Feb/22

	$I^{'} m n o t s u r e . I^{'} l l t r y u s i n g m a t r i x o p t i c s .$
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