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Two plano-convex lenses of focal lengths $f$ and $2 f$ are coaxially separated so that the spherical aberration is minimized. The effective focal length of the combination is :

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$d = f_2 - f_1$ $= 2f - f = f$
$f_{eq} = \dfrac {f_1f_2}{f_1 + f_2-d} = \dfrac {2f \times f}{f + 2f - f} = f$

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Two plano-convex lenses of focal lengths fff and 2f2 f2f are coaxially separated so that the spherical aberration is minimized. The effective focal length of the combination is :

d=f2−f1d = f_2 - f_1d=f2​−f1​ =2f−f=f= 2f - f = f=2f−f=ffeq=f1f2f1+f2−d=2f×ff+2f−f=ff_{eq} = \dfrac {f_1f_2}{f_1 + f_2-d} = \dfrac {2f \times f}{f + 2f - f} = ffeq​=f1​+f2​−df1​f2​​=f+2f−f2f×f​=f

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Two plano-convex lenses of focal lengths $f$ and $2 f$ are coaxially separated so that the spherical aberration is minimized. The effective focal length of the combination is :

$d = f_2 - f_1$ $= 2f - f = f$
$f_{eq} = \dfrac {f_1f_2}{f_1 + f_2-d} = \dfrac {2f \times f}{f + 2f - f} = f$