  In this paper, both edge and mixed metric dimensions of Johnson graphs
$J_{n,k}$ are considered. A new tight lower bound for $\beta_E(J_{n,k})$ based
on hitting sets has been obtained. Using this bound, exact values for
$\beta_E(J_{n,2})$ and $\beta_M(J_{n,2})$ have been derived, and it is proved
that $\beta_E(J_{n,2}) = \beta_M(J_{n,2})$.
