Question

Three perfectly polarizing sheets are spaced 2?cm {\rm cm} apart and in parallel planes. The transmission axis of the second sheet is 28 ? \deg relative to the first one. The transmission axis of the third sheet is 90 ? ^\circ relative to the first one. Unpolarized light impinges on the first polarizing sheet.

What percent of this light is transmitted out through the third polarizer?

Answer 1

I₃/Io % = 0.8.59

Step-by-step explanation:

A polarizer is a complaint sheet for light in the polarization direction and blocks the perpendicular one. When we use two polarizers the transmission between them is described by Malus's law

I = I₀ cos² θ

Let's apply the previous exposures in our case, the light is indicatively not polarized, so the first polarized lets half of the light pass

I₁ = ½ I₀

The light transmitted by the second polarizer

I₂ = I₁ cos² θ

I₂ = (½ I₀) cos2 28

The transmission by the polarizing third is

I₃ = I₂ cos² θ₃

The angle of the third polarizer with respect to the second is

θ₃ = 90-28

θ₃ = 62º

I₃ = (½ I₀ cos² 28 cos² 62)

Let's calculate

I₃ = Io ½ 0.7796 0.2204

I₃ = Io 0.0859

I₃/Io= 0.0859 100

I₃/Io % = 0.8.59