∵Three polarizers are arranged as shown in Figure 25-46 . If...

$\because$ Three polarizers are arranged as shown in Figure $25-46 .$ If the incident beam of light is unpolarized and has an intensity of $1.60 \mathrm{W} / \mathrm{m}^{2},$ find the transmitted intensity (a) when $\theta_{2}=25.0^{\circ}$ and $\theta_{3}=50.0^{\circ},$ and ( b ) when $\theta_{2}=50.0^{\circ}$ and $\theta_{3}=25.0^{\circ} .$

$\because$ Three polarizers are arranged as shown in Figure $25-46 .$ If the
incident beam of light is unpolarized and has an intensity of
$1.60 \mathrm{W} / \mathrm{m}^{2},$ find the transmitted intensity (a) when $\theta_{2}=25.0^{\circ}$
and $\theta_{3}=50.0^{\circ},$ and ( b ) when $\theta_{2}=50.0^{\circ}$ and $\theta_{3}=25.0^{\circ} .$

Key Concepts

Multiple Polarizer Arrangements

When light passes through multiple polarizers, the effect on the light’s intensity and polarization state accumulates. After the initial reduction from unpolarized light to linearly polarized light, subsequent polarizers further reduce the intensity based on their relative angles. Understanding how the orientation of each polarizer influences the final transmitted intensity is critical to solving problems involving multiple polarizers.

Unpolarized Light

Unpolarized light consists of waves vibrating in all directions perpendicular to its direction of propagation. When it passes through the first polarizer, only the component of light aligned with the polarizer's axis is transmitted, effectively reducing the intensity by half. This concept is fundamental to understanding how the intensity changes as light passes through successive polarizing filters.

Polarizer

A polarizer is an optical filter that allows light waves of a specific polarization to pass while absorbing or reflecting others. The axis of a polarizer determines the direction of the transmitted light’s vibration. In systems with multiple polarizers, the relative orientation of each polarizer’s axis plays a crucial role in determining the final transmitted intensity.

Malus' Law

Malus’ Law quantifies the relationship between the intensity of polarized light and the angle between the light’s polarization direction and the axis of a polarizer. It states that the transmitted intensity is proportional to the cosine squared of the angle between these directions. This mathematical relation is essential for calculating the intensity of light after passing through successive polarizers.

Transcript

00:01 Okay, so in this problem, we have a beam of unpolarized light, and we have three filters.

00:10 The first filter has an angle, let's call, teta 1 of 0 degrees with the vertical.

00:22 The second filter, let's call this filter blue.

00:25 He has an angle with the vertical that we're going to call teta 2, because we do not know yet what it is.

00:40 And the turn filter, which is going to be the green filter, also has an angle with the vertical that is, that we're going to call teta 3.

00:56 So what we have to calculate is a angle with the vertical that is, that we're going to call theta 3.

01:00 In here.

01:03 We have to calculate the intensity of the transmitted bin after passing for the three polarizers knowing that the initial intensity of the of the beam let's put in here this color the initial intensity is just 1 .6 watts per meter square.

01:30 So remember that to calculate the intensity of the beam after passing through the first polarizer, we just have the original intensity decreased by half because the beam was unpolarized light.

01:51 And when we passes unpolarized light through a polarizer, we have the original intensity decreases by half.

02:01 So this is intensity of the transmitted beam.

02:05 The transmitted beam.

02:08 The second polarizer we have y2 in here.

02:13 This is just y1, cosine square of theta 2...

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