Answer:
the percentage of light that gets through this combination is 9.38
Explanation:
Given the data in the question;
Let us represent the incident unpolarized light with [tex]I_0[/tex].
So, the amount of light intensity passing through the first polarizer will be;
[tex]I_1[/tex] = [tex]I_0[/tex] / 2 ------ let this be equation 1
An the amount of light intensity passing through the second polarizer will be;
[tex]I_2[/tex] = [tex]I_1[/tex]cos²θ
given that; the second one has its transmission axis at 30°
so, we substitute;
[tex]I_2[/tex] = [tex]I_1[/tex] × cos²( 30° )
[tex]I_2[/tex] = [tex]I_1[/tex] × 0.75
[tex]I_2[/tex] = 0.75[tex]I_1[/tex]
from equation; [tex]I_1[/tex] = [tex]I_0[/tex] / 2
[tex]I_2[/tex] = 0.75( [tex]I_0[/tex] / 2 )
[tex]I_2[/tex] = 0.375[tex]I_0[/tex] .
Now, the amount of light intensity passing through the third polarizer will be;
[tex]I_3[/tex] = [tex]I_2[/tex]cos² ( 90° - 30° )
[tex]I_3[/tex] = [tex]I_2[/tex] × cos²( 60° )
[tex]I_3[/tex] = [tex]I_2[/tex] × 0.25
we substitute
[tex]I_3[/tex] = 0.375[tex]I_0[/tex] × 0.25
[tex]I_3[/tex] = 0.09375[tex]I_0[/tex]
∴ [tex]I_3[/tex]/[tex]I_0[/tex] × 100 = 0.09375 × 100
⇒ 9.38%
Therefore, the percentage of light that gets through this combination is 9.38
