# How to use Malus's law to get real output energy from a polarizer

As we know, the Malus's law is:

$I=I_0\cos^2\theta$

Presently, I have a polarizer system (one half wave plate in front of a polarizer) in the lab, and have a powermeter. So, I can get two key factors: the input intensity of $I_0$ and rotated angle $\theta$. However, in real environment, the adjusted Malus's law will be:

$I=I_0\cos^2(\theta+\theta_0)+I_1$

In above equation, I is output intensity, $I_0$ is input intensity, $\theta_0$ is offset angle, $I_1$ is offset intensity.

Here, my question is: How can I fix the value of $I_1$ by testing?

Thanks.

## 1 Answer

Plot various $I$ against $\theta$ with as many intervals as possible and draw the general line of best fit for the $\cos^2(x)$ graph that should appear. The minimum point should be $I_1$. The difference between the first maximum and origin is $-\theta_0$

• Thanks friend! Actually, I measured the $I_1$ with increment of 5 degree. And the $I_1$ seemed without clear regularity. I will try to draw a plot. Thanks again. – Alex May 29 '17 at 15:05
• :) happy to help! Usually the initial conditions and unknown variables are obvious features on a graph – user86425 May 29 '17 at 16:13