Two Polaroids P_1 and P_2 are placed with their axis perpendicular to each other. Unpolarised light I_0 is incident on P_1. A third polaroid P_3 is…

Two Polaroids $\displaystyle \mathrm{P}_1$ and $\displaystyle \mathrm{P}_2$ are placed with their axis perpendicular to each other. Unpolarised light $\displaystyle \mathrm{I}_0$ is incident on $\displaystyle \mathrm{P}_1$. A third polaroid $\displaystyle \mathrm{P}_3$ is kept in between $\displaystyle P_1$ and $\displaystyle P_2$ such that its axis makes an angle $\displaystyle 45^{\circ}$ with that of $\displaystyle P_1$. The intensity of transmitted light through $\displaystyle \mathrm{P}_2$ is