Question

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?

Answer 1

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 $I_0$.

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;

$I_2$ = $I_1$cos²θ

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;

$I_3$ = $I_2$cos² ( 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