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

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_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