Two thin lenses of focal lengths f₁ and f₂ are in contact and coaxial. The power of the combination is

$square root of straight f subscript 1 over straight f subscript 2 end root$
$square root of straight f subscript 2 over straight f subscript 1 end root$
$fraction numerator straight f subscript 1 straight f subscript 2 over denominator straight f subscript 1 space plus straight f subscript 2 end fraction$
$fraction numerator straight f subscript 1 plus straight f subscript 2 over denominator straight f subscript 1 straight f subscript 2 end fraction$

Solution

fraction numerator straight f subscript 1 plus straight f subscript 2 over denominator straight f subscript 1 straight f subscript 2 end fraction

If two thin lenses of focal lengths f₁, f₂ are placed in contact coaxially, then equivalent focal length of combination is
$1 over straight F space equals 1 over f subscript 1 plus 1 over f subscript 2 minus fraction numerator 0 over denominator f subscript 1 f subscript 2 end fraction space equals space 1 over f subscript 1 plus 1 over f subscript 2 P o w e r space f o r space t h e space c o m b i n a t i o n space i s space P space equals space 1 over F space space equals 1 over f subscript 1 space plus 1 over f subscript 2 space equals space fraction numerator f subscript 1 plus f subscript 2 over denominator f subscript 1 f subscript 2 end fraction$

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