 Solution

For the convex vacuum void, use internal refractive index $1$, external refractive index $n$, and the original $\alpha >0$ in the immersed thin lens formula:A concave glass thin lens of the same curvature magnitude in vacuum has ${\alpha }_{\mathrm{concave}}=-\alpha$ and thereforeBoth elements diverge, but their physical focal lengths differ by a factor $n$ for $n>1$. For example, $n=1.5$ makes the void's focal length magnitude $1.5$ times that of the concave glass element. Their reduced optical powers $n_{\mathrm{outside}}/f$ are equal; physical focal length also depends on the surrounding refractive index.