A plano-convex lens (focal length f2, refractive index μ2, radius of curvature R) fits exactly into a plano-concave lens (focal length f1, refractive index μ1, radius of curvature R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be:

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A plano-convex lens (focal length f₂, refractive index μ₂, radius of curvature R) fits exactly into a plano-concave lens (focal length f₁, refractive index μ₁, radius of curvature R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be:

f₁ + f₂

$\frac{R}{μ_{2} - μ_{1}}$

$\frac{2 f_{1} f_{2}}{f_{1} + f_{2}}$

f₁ – f₂

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$\frac{1}{f} = \frac{(μ_{1} - 1)}{R} + \frac{(1 - μ_{2})}{R}$

$\frac{1}{f} = \frac{(μ_{1} - μ_{2})}{R}$

$\Rightarrow f = \frac{R}{μ_{1} - μ_{2}}$