A polarized light that has an intensity I0 = 52.0 W/m² is incident on four polarizing disks whose planes are parallel and centered on a common axis. Suppose that the transmission axis of the first polarizer is rotated 18° relative to the axis of polarization of the incident light, and that the transmission axis of each additional analyzer is rotated 18° relative to the transmission axis of the previous one. Calculate the transmitted intensity through all polarizers.

According to the malus law, when unpolarized or polarized light passes through polarizing disk, the intensity of the transmitted light is directly proportional to the square of the cosine of angle between the transmission axis and polarizer optic axis.

∴ [tex]I = I' cos^2\alpha[/tex]

Where [tex]I=[/tex] transmitted intensity, [tex]I'=[/tex] incident intensity, [tex]\alpha =[/tex] angle between the transmission axis and polarizer optic axis.

Here, there are four polarizing disks so that.

from first disk,

∴ [tex]I[/tex]₁ [tex]= 52 (cos)^2[/tex] 18°

= [tex]52[/tex]×[tex]0.904[/tex]

= [tex]47.01[/tex]

Now [tex]I[/tex]₁ behave as an incident light for second polarizer so we only multiply

[tex]cos^218[/tex] term

so we write,

∴ [tex]I[/tex]₂ = [tex]47.01[/tex]×[tex]0.904[/tex]

[tex]= 42.495[/tex]

From third polarizer,

∴ [tex]I[/tex]₃ = [tex]42.495[/tex]×[tex]0.904[/tex]

[tex]= 38.415[/tex]

From forth polarizer,

∴ [tex]I[/tex]₄ = [tex]38.415[/tex]×[tex]0.904[/tex]

[tex]= 34.73[/tex]

Therefor, the the transmitted intensity through forth polarizer = 34.73 [tex]W/m^2[/tex].