# Multiple Polarisers

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1. Sep 26, 2015

### Mnemonic

1. The problem statement, all variables and given/known data
You use a sequence of ideal polarising filters, each with its axis making the same angle with the axis of the previous filter, to rotate the plane of polarisation of a polarised light beam by a total of 45°. You wish to have an intensity reduction no larger than 10%.

What is the angle between multiple polarisers?

2. Relevant equations
I=Imaxcos2(θ)

3. The attempt at a solution
For multiple polarisers I=Imaxcos2*n(θ/n) where n is an integer

So I=cos2*n(θ/n) with I>0.9

The only integer solutions I was able to obtain was 9 polarisers separated by 5 degrees (n=9). This would give I=0.933 which is less than 10% loss if Imax=1.

However, this doesn't appear to be giving me the correct solution. What am I missing?

2. Sep 26, 2015

### TSny

Using the formula, I find that n = 9 is not the smallest integer value of n that will work. (θ does not need to be an integer number of degrees.)

3. Sep 27, 2015

### Mnemonic

Was using radians in solution. Thanks for making me look back and double-check!

4. Sep 27, 2015

OK. Good.