Solution:

An unpolarized light of intensity \(I_0\) becomes \(I_1 = \frac{I_0}{2}\) after passing through the first polarizer. According to Malus's Law, the final intensity is \(I_2 = I_1 cos^2(45^\circ) = \frac{I_0}{2} \left(\frac{1}{\sqrt{2}}\right)^2 = \frac{I_0}{4}\), which corresponds to \(25%\) of the incident intensity.