145k views
0 votes
Polarization: Unpolarized light passes through three ideal polarizing filters. The first filter is oriented with a horizontal transmission axis, the second one has its transmission axis at 30° from the horizontal, and the third filter has a vertical transmission axis. What percent of the light gets through this combination?

1 Answer

3 votes

Answer:

the percentage of light that gets through this combination is 9.38

Step-by-step explanation:

Given the data in the question;

Let us represent the incident unpolarized light with
I_0.

So, the amount of light intensity passing through the first polarizer will be;


I_1 =
I_0 / 2 ------ let this be equation 1

An the amount of light intensity passing through the second polarizer will be;


I_2 =
I_1cos²θ

given that; the second one has its transmission axis at 30°

so, we substitute;


I_2 =
I_1 × cos²( 30° )


I_2 =
I_1 × 0.75


I_2 = 0.75
I_1

from equation;
I_1 =
I_0 / 2


I_2 = 0.75(
I_0 / 2 )


I_2 = 0.375
I_0 .

Now, the amount of light intensity passing through the third polarizer will be;


I_3 =
I_2cos² ( 90° - 30° )


I_3 =
I_2 × cos²( 60° )


I_3 =
I_2 × 0.25

we substitute


I_3 = 0.375
I_0 × 0.25


I_3 = 0.09375
I_0


I_3/
I_0 × 100 = 0.09375 × 100

9.38%

Therefore, the percentage of light that gets through this combination is 9.38

User DaemonThread
by
7.5k points