$L_{S_{f}}=L_{S_{i}}\left[1+\alpha_{S} \Delta T\right]$

$\Rightarrow \Delta L_{\text {steel}}=L_{S_{i}} \alpha_{S} \Delta T$

$L_{C_{f}}=L_{C_{i}}\left[1+\alpha_{C} \Delta T\right]$

$\Rightarrow \Delta L_{\text {copper}}=L_{C_{i}} \alpha_{C} \Delta T$

For $\Delta L_{\text {steel }}=\Delta L_{\text {copper }}$

$\Rightarrow L_{S_{i}} \alpha_{S} \Delta T=L_{C_{i}} \alpha_{C} \Delta T$

$\Rightarrow \frac{L_{S_{i}}}{L_{C_{i}}}=\frac{\alpha_{C}}{\alpha_{S}}=\frac{1.8 \times 10^{-5}}{1.2 \times 10^{-5}}=\frac{3}{2}$

$\therefore \frac{L_{S_{i}}}{L_{C_{i}}}=\frac{3}{2}$ in $(1)$ only