Intensity of light passing through 3 polarizers

[ilovejava]

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

 

[Doc Al]

To find the intensity of the light that passes through the first polarizer I used Malus' Law and used the angle 33°.

Good.

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.

 

[.Scott]

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?

 

[Doc Al]

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!