Two Polaroids $P_1$, and $P_2$ are placed with their axis perpendicular to each other. Unpolarised light $I_o$ is incident on $P_1$. A third polaroid $P_3$, is kept in -between $P_1$, and $P_2$, such that its axis makes an angle $45^{\circ}$ with that of $P_1$. The intensity of transmitted Iight through $P_2$, is:

Question

$\begin{array}{1 1} (1) \frac{I_0}{2} \\ (2) \frac{I_0}{4} \\ (3) \frac{I_0}{8} \\ (4) \frac{I_0}{16} \end{array}$