Polarization I = Io*cos^2 theta

In summary, the problem involves two polarizers oriented at 38.8o to each other and plane-polarized light being incident on them. With the given equation and known values, the initial polarization direction of the incident light can be found by solving for the angle θ1.
  • #1
DAP1MP13
8
0
Two polarizers are oriented at 38.8o to each other and plane-polarized light is incident on them. If only 14.6 percent of the light gets through both of them, what was the initial polarization direction of the incident light?

Ok, I'm not exactly sure what this problem is asking for, do they want an angle or what?

So basically the only equation given for this section is I = Io*cos^2 theta.
I did ((cos*38.8)^2)((cos*38.8)^2) = .369...

I don't see how I can solve the problem with just this, I thought maybe I can relate it to Snell's eq., but there is no index (n) given.
Also I know that I-final = 14.6% = .146, but once again I don't really know what to do with this.

Any hints and help will be greatly appreciated.
Thanks...
 
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  • #2
That equation, the law of Malus, tells you what percentage (of the intensity) of a polarized light beam gets through a polarizer set at an angle of [itex]\theta[/itex] to the incident beam's plane of polarization. (And realize that when a beam passes through a polarizer, the part that survives is totally polarized along the axis of the polarizer.)

You figured out the percentage that got throught the second polarizer. So what must have been the percentage that got through the first? (You know the net percentage that got through.)
 
  • #3
Thanks Doc Al

So the net amount that got through both polarizers was .369, but it says that .146 got through.
The amount that went throught the first would just be (cos38.8)^2 = .607.

I still don't know how this would help me to get the answer...
Through 1st polarizer => .607
Through 2nd polarizer => .369 or .146
How would this information tell you what was the initial polarization direction of the incident light?
 
  • #4
Can I get some more help on this please?

Thanks
 
  • #5
DAP1MP13 said:
Two polarizers are oriented at 38.8o to each other and plane-polarized light is incident on them. If only 14.6 percent of the light gets through both of them, what was the initial polarization direction of the incident light?

Ok, I'm not exactly sure what this problem is asking for, do they want an angle or what?

So basically the only equation given for this section is I = Io*cos^2 theta.
I did ((cos*38.8)^2)((cos*38.8)^2) = .369...

I don't see how I can solve the problem with just this, I thought maybe I can relate it to Snell's eq., but there is no index (n) given.
Also I know that I-final = 14.6% = .146, but once again I don't really know what to do with this.
there are 2 angles involved in this problem.
first, the 2 polarizers are rotated relative to one another by angle θ2=38.8°
then, the plane polarized incident light is rotated relative to the first polarizer by angle θ1.
the total net transmission thru both polarizers is given to be 0.146, so the transmission equation is:
I = I0cos21)cos22)
or rearranging and placing known values into the equation:
I/I0 = 0.146
= cos21)cos22)
= cos21)cos2(38.8°)

cos21) = (0.146)/cos2(38.8°)
cos(θ1) = SQRT{(0.146)/cos2(38.8°)}

Now solve for θ1 to find the incident light angle (relative to first polarizer).
 

1. What is polarization?

Polarization refers to the orientation of the electric field in an electromagnetic wave. In other words, it describes the direction in which the electric field is oscillating.

2. What is the equation for polarization intensity?

The equation for polarization intensity is I = Io*cos^2 theta, where I is the intensity of the polarized light, Io is the maximum intensity of the unpolarized light, and theta is the angle between the direction of polarization and the direction of the incident light.

3. How does polarization affect light?

Polarization can affect the intensity, direction, and color of light. It can also determine how the light will interact with different materials, such as filters or reflective surfaces.

4. What is the difference between linear and circular polarization?

Linear polarization refers to light waves that vibrate in a single plane, whereas circular polarization refers to light waves that rotate in a circular motion. Linear polarization can be further divided into horizontal and vertical polarization, while circular polarization can be clockwise or counterclockwise.

5. What are some applications of polarization?

Polarization has various applications in technology and everyday life. It is used in sunglasses and camera filters to reduce glare, in 3D glasses to create a sense of depth, and in optical instruments to analyze materials and measure stress. It also plays a crucial role in satellite communication and radar technology.

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