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 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 light through $P_2$ is:

1. A
   $\frac{I_0}{20}$
2. B
   $\frac{I_0}{40}$
3. C
   $\frac{I_0}{80}$
4. D
   $\frac{I_0}{8}$