Intensity of light passing through polarising filters

This is easily explained using Malus' law, $I=I_0cos^2theta$, where $I$ is the transmitted intensity, $I_0$ is the initial intensity and $theta$ is the angle between the pass axis of the polarizer and the polarization axis of light. Supposing the first filter to have been rotated by 45 degrees, we have $I_1=frac{I_0}{2}$. Since the final filter now makes an angle of 45 with the second one, $I_2=I_1cos^245^o=frac{I_0}{4}>0$, representing an increase.

The point is that the polarization of light changes after passing through the first polarizer-which is to say, it changes from horizontal to a 45 degree one (which in turn makes it 45 degrees with respect to the second polarizer). Had it been that (half) the light passes through the first polarizer and remains horizontally polarized, we would have retained the intuitive result that the final transmitted intensity is zero.