Step 1: Acidified potassium dichromate ($K_2Cr_2O_7$) acts as a strong oxidizing agent.
Step 2: In acidic medium, iodide ions ($I^-$) are oxidized to iodine ($I_2$), while dichromate ions are reduced.
Step 3: Oxidation states:
\[
Cr \text{ in } Cr_2O_7^{2-} = +6
\]
Step 4: During the reaction, chromium gets reduced to $Cr^{3+}$.
Step 5: Balanced ionic equation:
\[
Cr_2O_7^{2-} + 6I^- + 14H^+ \rightarrow 2Cr^{3+} + 3I_2 + 7H_2O
\]
Step 6: Hence, chromium in the final product exists as $Cr^{3+}$.
Therefore, oxidation state of chromium is $+3$.