  We undertake a theoretical analysis to probe the Kerr spectrum within the
superconducting phase of strontium ruthenate, where the Kerr rotation
experiments demonstrate the existence of a superconducting state with broken
time reversal symmetry. We find that spin-orbit coupling changes the
hybridization along the Fermi surface's diagonal zone mainly affects Hall
transport. We show that the dominant Hall response arises mainly from the
quasi-1D orbitals $d_{yz}$ and $d_{xz}$, linked to their hybridization, while
other contributions are negligible. This establishes that, the breaking of time
reversal symmetry of quasi-1D orbitals can account for the existence of the
Kerr angle, irrespective of the order symmetry specific to the $d_{xy}$
orbital. Moreover, the optical Hall conductivity and Kerr angle estimated for
the hypothesised superconducting orders also closely match the experimental
findings, providing important novel insight on the role of the spin-orbit
coupling, hybridization, and emergent order.
