Two Polaroids P _ 1 and P _ 2 are placed with their axis...

Two Polaroids ${P}_{1}$ and ${P}_{2}$ are placed with their axis perpendicular to each other. Unpolarised light with intensity ${I}_{0}$ 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 ${45}^{\text{o}}$ with that of ${P}_{1}$. The intensity of transmitted light through ${P}_{2}$ is