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

A

$$\frac {I_0}{8}$$

B

$$\frac {I_0}{16}$$

C

$$\frac {I_0}{2}$$

D

$$\frac {I_0}{4}$$