Calculate Angle for Multiple Polarisers to Reduce Intensity <10%

[Mnemonic]

Homework Statement

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?

Homework Equations

I=I_maxcos²(θ)

The Attempt at a Solution

For multiple polarisers I=I_maxcos^2*n(θ/n) where n is an integer

So I=cos^2*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 I_max=1.

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

 

[TSny]

So I=cos^2*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).

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.)

 

[Mnemonic]

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.)

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

 

[TSny]

OK. Good.