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SERPSE$1037\mathrm{.}6.$OP$\mathrm{.}025.$MI$.$

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 $I_i=15\mathrm{.}0$ units $($arbitrary$).$ Calculate the transmitted intensity $I_f$ when ${}_1=17\mathrm{.}0,{}_2=37\mathrm{.}0,$ and ${}_3=63\mathrm{.}0.$ Hint: Make repeated use of Malus's law.

$I_f=,$ units

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