Unpolarized light is incident on four polarizing sheets with their transmission axes oriented as shown in the figure, in which θ1 = 27.0° and θ2 = 50.0°. What percentage of the initial light intensity is transmitted through this set of polarizers?

Answer 1

If polarized light of intensity I₀ is incident on a polarizing sheet, the intensity transmitted by
the sheet depends on the angle between the polarization direction of the light and the transmission axis of the sheet, φ, via
I= I₀•cos²φ.

After the 1st sheet
I₁=0.5•I₀.

After the 2nd sheet
I₂=I₁•cos²φ₁=0.5•I₀•cos²27°=0.397•I₀.

After the 2nd sheet
I₃=I₂•cos²φ₂=0.397•I₀•cos²(50-27)°=0.336•I₀.

After the 3rd sheet
I₄=I₃•cos²φ₃=0.336•I₀•cos²(90-50)°=0.197•I₀.

(I₄/I₀)•100%= 19.7%