For ${\mathrm{Na}}^{+}, {\mathrm{Mg}}^{2+}, {\mathrm{F}}^{-}$ and ${\mathrm{O}}^{2-}$; the correct order of increasing ionic radii is  

Each species has an identical electrical structure $\left(10{\mathrm{e}}^{-}\right)$

The greater the positive change, the smaller the ionic radii of isoelectronic species. 

For isoelectronic species, larger ionic radii correspond to greater negative change.

Hence the order is ${\mathrm{Mg}}^{2+}<{\mathrm{Na}}^{+}<{\mathrm{F}}^{-}<{\mathrm{O}}^{2-}$

Hence, the required option is C.