How can I compute the intensity of a polarized wave going through a Polaroid?

1 Answer
Dec 21, 2014

You could use Malus' Law.
Malus' Law tells us that if you have a polarized wave (of intensity I_0) passing through a polarizer the emerging intensity ( I ) will be proportional to the cosine squared of the angle between the polarizing direction of the incoming wave and the axis of the polarizer.

Or: I=I_0*cos^2(theta)

Sounds difficult but look at the picture:
enter image source here

Knowing the angle theta and the incoming intensity you´ll be able to evaluate the output intensity.

Special case :
When you have unpolarized light falling upon the polarizer the transmitted intensity will be 1/2 of the incoming intensity, i.e.:
I=I_0/2
(to understand this, look at the mathematical explanation that follows and remember that the average value of cos^2 is 1/2!!!)

As a mathematical explanation you have:
If E0 is the amplitude of the electric vector of the incoming wave, then the intensity I_0 of the wave incident on the polarizer is proportional to E0^2.

The electric field vector E0 of the incoming wave can be resolved into two rectangular components projected upon the polarizer axis:
E0*cos(theta) and E0*sin(theta)
The analyzer will transmit only the component ( i.e E0*cos(theta)) which is parallel to its transmission axis.
enter image source here
But intensity is proportional to the square of the electric vector you have:
IpropE^2 and:
Iprop(E0*cos(theta))^2 but:
I/I_0=(E0*cos(theta))^2/(E0^2)

and finally:
I=I_0*cos^2(theta)