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Three polarizing plates whose planes are parallel are centered on a common axis. The directions of the transmission axes relative to the common vertical direction are shown in the figure below. A linearly polarized beam of light with plane of polarization parallel to the vertical reference direction is incident from the left onto the first disk with intensity $1.$ What is the transmitted intensity $1?$ Hint: Make repeated use of Malus's law.

A$.I_{i}co{s}^2{}_3$

B$.I_{i}co{s}^2{}_{1}co{s}^2{}_{2}co{s}^2{}_3$

C$.I_{i}co{s}^2{}_{1}co{s}^2({}_2-{}_1)co{s}^2({}_3-{}_2)$

D$.I_i$

E$.\frac{I_i}{cos{}_3}$

$6$