As Shown in the Figure, the Orientation of the Transmission $1.00 \mathrm {~kW} / \mathrm { m } ^ { 2 }$

As shown in the figure, the orientation of the transmission axis for each of three ideal polarizing sheets is labeled relative to the vertical direction. A beam of light, polarized in the vertical direction, is incident on the first polarizer with an intensity of $1.00 \mathrm {~kW} / \mathrm { m } ^ { 2 }$ . What is the intensity of the beam after it has passed through the three polarizing sheets when $\theta _ { 1 } = 30 ^ { \circ } , \theta _ { 2 } = 30 ^ { \circ }$ , and $\theta _ { 3 } =$ $60 ^ { \circ }$ ?

A) $433 \mathrm {~W} / \mathrm { m } ^ { 2 }$
B) $141 \mathrm {~W} / \mathrm { m } ^ { 2 }$
C) $316 \mathrm {~W} / \mathrm { m } ^ { 2 }$
D) $563 \mathrm {~W} / \mathrm { m } ^ { 2 }$
E) $188 \mathrm {~W} / \mathrm { m } ^ { 2 }$