The average value of cos^2(phi) is 1/2.

[Lindsayyyy]

Hi,

Homework Statement

I have the following question:

I found two formulas given for the intensity after polarised light went through a polarisation filter.

Homework Equations

$$I_{1}=I_{0}*\frac 1 2$$

and

$$I_{1}= I_{0}*cos^{2}(\phi)$$

The Attempt at a Solution

Well I don't know when to use which equation. Does it depend on the filter used or does it depend on the angle?
Thanks for your help

edit:

I think when the axis of the filter is parallel to the incoming rays its just 1/2 and when there's an angle between the incoming rays and the filter I have to use the one with cosine.

 

[IDOGAWACONAN]

The first one is used when the light is natural light;
And use the second when it is linearly polarized light.

 

[berkeman]

Hi,

Homework Statement

I have the following question:

I found two formulas given for the intensity after polarised light went through a polarisation filter.

Homework Equations

$$I_{1}=I_{0}*\frac 1 2$$

and

$$I_{1}= I_{0}*cos^{2}(\phi)$$

The Attempt at a Solution

Well I don't know when to use which equation. Does it depend on the filter used or does it depend on the angle?
Thanks for your help

edit:

I think when the axis of the filter is parallel to the incoming rays its just 1/2 and when there's an angle between the incoming rays and the filter I have to use the one with cosine.

The first one is used when the light is natural light;
And use the second when it is linearly polarized light.

As IDOG says, the first equation is for unpolarized light incident on the polarizer, and the 2nd is for polarized light with its axis of polarization at an angle phi to the polarizer's axis.

You can use the 2nd equation to derive the first equation, BTW. What is the average value of cos^2(phi) ?