Intensity of light passing through 3 polarizers

In summary: So the transmitted intensity through all three polarizers is given by I = I0cos2(33)cos2(54)cos2(46). In summary, the transmitted intensity through all three polarizers is equal to the initial intensity (I0) multiplied by the cosines of the angles between each successive polarizer, starting with the angle of the incident light and ending with the angle of the final polarizer.
  • #1
ilovejava
21
0

Homework Statement


Three polarizing disks whose planes are parallel and centered on common axis. The directions of their transmission axes relative to the vertical are respectively: θ1 = 33° clockwise, θ2 = 21° counter-clockwise, and θ3 = 25° clockwise. A beam of light polarized along the vertical is incident onto the first polarizer with an intensity of I0 = 26 W/m². Calculate the transmitted intensity through all three polarizers.

Homework Equations


S=S0cos2θ

The Attempt at a Solution


I recognize that the light passing through the polarizers has already been polarized. To find the intensity of the light that passes through the first polarizer I used Malus' Law and used the angle 33°. I am not sure how to deal with the angles of the remaining two polarizers to find the total transmitted intensity through all three polarizers.

EDIT: The angle θ is the angle made between the axis of polarization of the light and axis of transmission of the polarizer. According to that logic I came up with the conclusion that

I0cos2(33)cos2(54)cos2(46)

54 is the angle made between 33° clockwise and 21° counter-clockwise, and 46 is the angle made between 21° clockwise and 25° clockwise
 
Last edited:
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  • #2
ilovejava said:
To find the intensity of the light that passes through the first polarizer I used Malus' Law and used the angle 33°.
Good.

ilovejava said:
I am not sure how to deal with the angles of the remaining two polarizers to find the total transmitted intensity through all three polarizers.
Do the same thing, only realize that after the beam passes through the first polarizer it is polarized in a new direction, given by the angle of the polarizer. Treat each passing the same way.
 
  • #3
The light incident on the seconds polarizer is also polarized - but not along the vertical axis. What is it's angel relative to the second polarizer?
 
  • #4
ilovejava said:
EDIT: The angle θ is the angle made between the axis of polarization of the light and axis of transmission of the polarizer. According to that logic I came up with the conclusion that

I0cos2(33)cos2(54)cos2(46)

54 is the angle made between 33° clockwise and 21° counter-clockwise, and 46 is the angle made between 21° clockwise and 25° clockwise
Good!
 

FAQ: Intensity of light passing through 3 polarizers

1. What is the definition of intensity of light?

The intensity of light is the amount of energy per unit time that is transmitted through a given area in a specific direction. It is typically measured in units of watts per square meter (W/m²).

2. How do polarizers affect the intensity of light passing through them?

Polarizers are filters that only allow light waves with a specific orientation to pass through. As a result, they can reduce the intensity of light passing through them by blocking or absorbing certain wavelengths or orientations of light.

3. What happens when multiple polarizers are placed in a series?

When multiple polarizers are placed in a series, the intensity of light passing through them decreases with each additional polarizer. This is because each polarizer is blocking a portion of the light that passes through the previous polarizer, resulting in a net decrease in intensity.

4. Is there a limit to how much the intensity of light can decrease when passing through multiple polarizers?

Yes, there is a limit to how much the intensity of light can decrease when passing through multiple polarizers. Eventually, all of the light will be blocked or absorbed by the polarizers, resulting in no light passing through.

5. Can the intensity of light passing through polarizers be increased?

No, the intensity of light passing through polarizers cannot be increased. Polarizers can only decrease the intensity of light by blocking or absorbing certain wavelengths or orientations of light. Once the light has been reduced, it cannot be increased again by the polarizers.

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