Answer:
[tex]0.293I_0[/tex]
Explanation:
When the unpolarized light passes through the first polarizer, only the component of the light parallel to the axis of the polarizer passes through.
Therefore, after the first polarizer, the intensity of light passing through it is halved, so the intensity after the first polarizer is:
[tex]I_1=\frac{I_0}{2}[/tex]
Then, the light passes through the second polarizer. In this case, the intensity of the light passing through the 2nd polarizer is given by Malus' law:
[tex]I_2=I_1 cos^2 \theta[/tex]
where
[tex]\theta[/tex] is the angle between the axes of the two polarizer
Here we have
[tex]\theta=40^{\circ}[/tex]
So the intensity after the 2nd polarizer is
[tex]I_2=I_1 (cos 40^{\circ})^2=0.587I_1[/tex]
And substituting the expression for I1, we find:
[tex]I_2=0.587 (\frac{I_0}{2})=0.293I_0[/tex]
