Answer:
I₄ / Io = 0.388 = 38.8%
Explanation:
For this exercise we will analyze the effect of having two depolarizers with an annulus between them, this is described by Malus's law
I = Io cos² θ
where tea is the angle between the two polarizers.
For this case we must apply this law to each pair of polarizers.
The light that reaches the first polarizer is non-polarized light, therefore only the light that has polarization is transmitted in the direction of the depolarizer, which is horizontal.
I₁ = I₀ / 2
this intnesidad reaches the second polarizer that has an angle of 23º with respect to the first polarizer
I₂ = I₁ cos² 23
I₂ = I₀ / 2 0.847
This light reaches the third polarizer, which has an angle of 42º with respect to the first polarized one.
Let's find the angle with respect to the 2nd polarizer
θ = 42- 23
θ = 19º
we apply the law of Malus
I₃ = I₂2 cos 19
I₃ = I₀ 0.847 / 2 0.9455
I₃ = Io 0.4
This intensity of light reaches the fourth polarizer, with an angle of 14º with respect to the 3polarizer
I₄ = Io 0.4 cos 14
I₄ = Io 0.4 0.970
I₄ = Io 0.388
to give this result as a percentage
I₄ / Io = 0.388 = 38.8%
