A polarizing filter is a plastic sheet that allows only certain components of the electric field in an electromagnetic wave to pass through, and a wave that has passed through such a filter is said to be polarized. After an initially unpolarized wave has passed through the filter shown in Figure P30.63a, for instance, the wave's electric field contains only the vertical components of all the electric field vectors present before the wave passed through. Because the horizontal components have been blocked, the wave has lost half of its initial intensity. If this polarized wave then passes through the filter of Figure P30.63b, where the filter-polarizing direction is at an angle \(\theta\) to the direction of the vertically polarized wave, the wave loses more of its intensity. If the polarized wave has an intensity \(S_{\text {before }}=200 \mathrm{~W} / \mathrm{m}^{2}\) before passing through the filter of Figure P30.63b and \(\theta=20.0^{\circ}\), what is the intensity after the wave passes through?

Data from Figure P30.63

(b) (a) Ebefore Eafter polarizing axis of filter polarizing axis of filter