Respuesta :
Answer:
Explanation:
Intensity of unpolarised light = Iā
intensity after passing through first polariser = Ā Iā / 2
Angle between first and second polariser is Ā Ļ so
intensity after passing through second polariser
= (Iā / 2) cosĀ²Ļ
Now angle between second and third polariser
= 90 - Ļ
intensity after passing though third polariser
= (Iā / 2) cosĀ²Ļ cosĀ²( 90 - Ļ)
= (Iā / 2) cosĀ²Ļ sinĀ²Ļ
= (Iā / 8) 4cosĀ²Ļ sinĀ²Ļ
= (Iā / 8) sinĀ²2Ļ
The intensity after the third polarizer will be:
Iā = (Iā/8)*sin^2(2Ļ)
What is the resulting intensity?
For non-polarized light that passes through any polarizer, we say that the intensity is reduced to its half.
Original intensity = Iā
After the first polarizer, the intensity will be:
Iā = Iā/2.
Now, when it passes through a polarizer such that the difference in angles with the polarization is x, the new intensity will be:
Iā = Iā*cos^2(x).
The angle between the second and the first polarizer is Ļ, then we have:
Iā = (Iā/2)*cos^2(Ļ).
Now we also know that the first and the last polarizer are crossed (so there is an angle of 90Ā°). Then if we define Īø as the angle between the second and the third polarizer, we will have that:
Ļ + Īø = 90Ā°
then:
Īø = 90Ā° - Ļ
The intensity after the third polarizer will be:
Iā = (Iā/2)*cos^2(Ļ)*cos^2(90Ā° - Ļ)
And we know that:
cos(90Ā° - Ļ) = sin(Ļ)
Then we can rewrite:
Iā = (Iā/2)*cos^2(Ļ)*sin^2(Ļ)
But we want a single trigonometric function, then we use the relation:
cos^2(Ļ)*sin^2(Ļ) = sin^2(2Ļ)/4
And replacing that, we get:
Iā = (Iā/2)*sin^2(2Ļ)/4 = (Iā/8)*sin^2(2Ļ)
If you want to learn more about light, you can read:
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