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 45º with that of $P_1$. The intensity of transmitted light through $P_2$ is

Question

( A ) $\frac{I_0}{8}$
( B ) $\frac{I_0}{2}$
( C ) $\frac{I_0}{4}$
( D ) $\frac{I_0}{16}$