Quick Microwave Optics question - Malus' Law

[satchmo05]

Homework Statement

I am needing to check my results against Malus' Law --> [I = I_ocos²(theta)]

I am unsure how to get I_o. So I have found my signal readings on the microwave detector and I know the angle that I rotated the microwave transmitter. I experimentally know the relationship between my signal reading and signal intensity. I just don't know how to verify my results with Malus' Law - meaning what is I_o?

Homework Equations

My signal-intensity relationship --> I = S^1.396648
Malus' Law --> I = I_ocos²(theta)

The Attempt at a Solution

So I know my set (12 values) of converted intensities and I know my 12 values of theta, so the only thing I don't know is the initial intensity, I_o. Is this something that is a specification of the device or is this experimental? Please let me know how to determine I_o. Thank you in advance for all help!

 

[fzero]

If you find that the plot of your I vs. \cos^2\theta values is linear, with zero intercept (within experimental uncertainties), then I_0 is the slope. Alternatively, you would have made a measurement at \theta=0 and used the slope of the graph as a consistency check.

 

[satchmo05]

So your first suggestion did not end up working unfortunately. When I graph my data of I against cos2(theta), I get a scatter plot shape similar to that of a logarithmic. In regards to your second suggestion, I don't think that would work either. Yes, I did make a measurement at theta = 0 [deg] (I made signal reading measurements from 0 - 85 [deg] in increments of 5 [deg]), but I wouldn't see the relation in doing that...

 

[Redbelly98]

What is cosθ, when θ is 0°?

And by extension, I = ____?

 

[satchmo05]

Ah, so the cos(theta) simply makes I a fraction of Io?

 

[Redbelly98]

Ah, so the cos(theta) simply makes I a fraction of Io?

Yes.

EDIT
Yes, if you mean cos²θ

 

[satchmo05]

I definitely understand where you're coming from. However, after creating an equation that relates my signal readings (in [mA]) and my intensities (in [W/m^2]), that equation ends up being S^1.396648. After comparing my results with what you just stated, I am not getting similar results (as I should be). What is wrong here? Thanks again.