Question

Unpolarized light is incident upon two polarization filters that do not have their transmission axes aligned. If 21% of the light passes through, what is the measure of the angle between the transmission axes of the filters?

Answer 1

When unpolarized light passes through two polarization filters with misaligned transmission axes, only a fraction of the light is transmitted. The measure of the angle between the transmission axes can be determined using Malus' Law.

Step-by-step explanation:

When unpolarized light is incident upon two polarization filters that do not have their transmission axes aligned, the intensity of the transmitted light is given by Malus' Law, which states that I = I0 * cos2(θ), where I0 is the initial intensity of the light and θ is the angle between the transmission axes of the filters.

Given that 21% of the light passes through, we can write the equation as 0.21 = cos2(θ). Taking the square root of both sides, we get 0.459 = cos(θ). Solving for θ, we find θ ≈ 63.4°.

Therefore, the measure of the angle between the transmission axes of the filters is approximately 63.4°.

Answer 2

49.6°

Step-by-step explanation:

`I_0` = Unpolarized light

`I_2` = Light after passing though second filter =
`0.21I_0`

Polarized light passing through first filter

`I_1=(I_0)/(2)`

Polarized light passing through second filter

`I_2=(I_0)/(2)cos^2\theta\\\Rightarrow 0.21I_0=(I_0)/(2)cos^2\theta\\\Rightarrow cos^2\theta=(0.21I_0)/((I_0)/(2))\\\Rightarrow cos\theta=\sqrt{(0.21I_0)/((I_0)/(2))}\\\Rightarrow \theta=cos^(-1)\sqrt{(0.21I_0)/((I_0)/(2))}\\\Rightarrow \theta=cos^(-1)√(0.21* 2)\\\Rightarrow \theta=cos^(-1)√(0.42)\\\Rightarrow \theta=49.6^(\circ)`

The angle between the two filters is 49.6°