If we have two converging thin lenses of focal lengths f1 and f2 respective, it is easy to determine what the effective focal length of the set, if the distance d between the optical centers of both lenses is negligible in relation to their focal lengths. That is, both are practically in contact. This will be the situation when we study the case of close-up lenses.
Gauss equation for the lens 1 will be:
1 1 1 --- +
--- --- s1 = f1
s'1 1 1 1
From this it follows that --- = - - - --- (1)
; s1 f1 s'1
La ecuación Gauss lens for it will be 2: 1
January 1
--- + ---- = - -
s2 s'2 f2
1 January 1
From this it follows that --- = --- - ---
s2 f2 S'2
But as the image point to the first lens becomes the object point for the second lens and the distance measured-to-object points from the optical center to the left, you verify that s2 =-s '1.
1 ; 1 1 1 1
Therefore: --- = ---- - --- ; = ---- + ---- (2)
s'2 f2 (-s'1) f2
s'1
Gauss equation for the combination of both lenses is:
January 1 1
------ = ---- + ----
fefec , s1
S'2
Substituting the values \u200b\u200bof equations (1) and (2) then:
1 , January 1
----- = --- + ----
fefec f1 f2
f1 f2
o lo que es lo mismo: fefec = -----------
f1 + f2
This equation will allow us to detemine the effective focal length of a lens which has been on the front COUPLING close-up lens.
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