Polarization between 3 sheets intensity

[Taylor_1989]

Homework Statement

Hi guys I am having a problem with this question

Q55 a) and b)

My problem is that for part a) I used the following logic. That if two sheet won't let light through at $90^\circ$ so if a 3rd sheet is inserted between the two the angle between each is $45^\circ$, But for part a) ans b)seem to be getting something wrong. I assume the the light I will show my working below.

Homework Equations

$I=I_0cos^2\theta$

The Attempt at a Solution

[/B]
a) light from sheet 1 to sheet 2 is:

$I_{1,2}=I_0(cos45)^2=\frac{I_0}{2}$

light from sheet 2 to sheet 3 is:

$I_{2,3}=\frac{I_0}{2}(cos45)^2=\frac{I_0}{4}$

but the ans is \frac{I_0}{8}

which is where I am confused is the first sheet be put at and angle of 45 degrees when light enters beacuse I was under the assumption the the first sheet is perpendicular to the last sheet at it is the sheet in the middle that is only 45 degrees.

I am having the same issue with b) thus why I have no workings

 

[gneill]

The $I_o$ in the law of Malus is usually taken to be the light intensity after the first polarizer. You need to first find out how that $I_o$ relates to the initial incident unpolarized light intensity

 

[Taylor_1989]

Ah yes I see now, that on average the electric field is 45 degree w/r to the trasmission axis. So the through the firs filter it would be $I=I_0\frac{1}{2}$

thank you very much for your help