College Physics (4th Edition)

The intensity transmitted through the second sheet is not necessarily zero. It is possible that some light gets through. When the light shines through the first polarizing sheet, an intensity of $I' = I_0~cos^2~\theta_1$ gets through, where $\theta_1$ is the angle between the initial polarity of the light and the polarizing sheet. When the light shines through the second polarizing sheet, an intensity of $I'~cos^2~\theta_2$ gets through, where $\theta_2$ is the angle between the polarity direction of the two polarizing sheets. As long as neither angle is $90^{\circ}$, then some of the light will get through the second polarizer.