What is the minimum number of Polarizers needed

[ah011]

Homework Statement

A polarized light is incident on several polarizing disks whose planes are parallel and centred on common axis. Suppose that the transmission axis of the first polarizer is rotated 25° relative to the axis of polarization of the incident light, and that the transmission axis of each additional analyzer is rotated 25° relative to the transmission axis of the previous one. What is the minimum number of polarizer needed (whole number), so the transmitted light through all polarizing sheets has an intensity that is less than 9% that striking the first polarizer?

Homework Equations

The Attempt at a Solution

Since the question is asking for the number of polarizers needed, you start by looking at 25 degrees take the cos^2(25). Then, since they are parallel and centered on a common axis it must be added to cos^2(25-9). I am not sure what to do after this.

 

[ah011]

Can anyone reply this question is making me tear my hair out

 

[Qwertywerty]

Hint : Intensity after passing through one polarizer is I₀cos²25⁰, after the second, I₀cos⁴25⁰, ...Do you see a general formula for the intensity after passing through x polarizers?

Also, you typically don't want to be the first one to reply to your own thread. It is no longer visible in the 'Unanswered Threads' column, and people are less likely to visit this thread.

 

[haruspex]

Then, since they are parallel and centered on a common axis it must be added to cos^2(25-9).

That's a very strange conclusion. Where did you get the 9 degrees from? It makes me think you misunderstand the arrangement.