Question

If plane polarized light is sent through 2 polarizers, the first at 45degrees to the original plane of polarization and the second at 90degrees to the original plane of polarization. What fraction of the original polarized intensity passes through the last polarizer?

Answer 1

From Malus' law, the intensity of the light transmitted through a polarizer (analyzer) having its transmission axis oriented at angle $45\degree$ to the plane of polarization of the incident polarized light is 

$$I=I_{max}cos^245\degree= \dfrac{I_{max}}{2}$$

Therefore, the intensity passing through the second polarizer having its transmission axis oriented at angle $\theta=(90\degree-45\degree)=45\degree$ is

$$I=\dfrac{I_{max}}{2}cos^245\degree=\dfrac{I_{max}}{4}$$

Hence, the intensity passing through the second polarizer is $\dfrac{I_{max}}{4}$