A beam of unpolarized light of intensity I0 passes through a series of ideal polarizing filters

A beam of unpolarized light of intensity I0 passes through a...

Key Concepts

Polarization of Light

Polarization refers to the orientation of the oscillations of the electromagnetic field in a light wave. When light is polarized, its electric field oscillates predominantly in one direction, which is crucial in understanding how light interacts with polarizing filters.

Unpolarized Light

Unpolarized light contains waves with electric fields oscillating in all directions perpendicular to the direction of propagation. When such light passes through a polarizer, only the component aligned with the polarizer’s axis is transmitted, typically resulting in a reduction of the light's intensity by a factor determined from averaging over all possible orientations.

Polarizing Filters

Polarizing filters are optical devices that allow light waves of a specific polarization direction to pass while blocking or absorbing others. Their impact on light intensity and polarization is determined by the relative angle between the incoming light’s polarization direction and the filter’s axis.

Malus's Law

Malus's Law provides the relationship between the intensity of polarized light before and after passing through a polarizer. It states that the transmitted intensity is proportional to the cosine squared of the angle between the light’s polarization direction and the axis of the polarizer, fundamental for calculating the intensity at successive points through a series of polarizers.

Intermediate Polarizers

Inserting an additional polarizer between two polarizers that are oriented at an angle relative to each other can allow some light transmission that would otherwise be completely blocked. This occurs because the intermediate polarizer reorients the polarization of the light gradually, which is an essential concept in manipulating the final intensity in a multi-polarizer setup.

Transcript

00:01 In this problem we have this incident light with intensity i0 and we want to compute what is intensity of the light at point a, b and t.

00:17 These points are separate by polarizers and the red lines represent the polarizing direction of the polarizers.

00:30 Well, in this kind of problems, we must distinguish two cases.

00:35 First, when the incident light is unpolarized, and second, when the incident light has a special polarizing direction.

00:49 In this problem, we are told that the incident light is unpolarized.

00:53 This is the simple of unpolarized light.

00:57 When this happened, only half of the incident light pass through the polarizer.

01:05 So the intensity of light at point a is just a zero over two.

01:13 In the direction of the electric field is the same as the direction of the polarizer.

01:21 So this is the direction of the electric field at point a.

01:26 This is vertical.

01:28 Well, now the light is not unpolarized anymore.

01:35 So we are in the second case.

01:38 When this happened and we want to compute what is the intensity of the light that pass through a polarizer, we need to compute what is the angle between the incident electric field and the polarizing direction of the polarizer.

01:56 In this case, this angle is the angle.

01:59 Is this, the angle is this, and we can see easily that this is 60 degrees, it's the same that this angle.

02:12 Well, now we can compute where is the intensity of the light at this point, and the intensity of the light is just the initial intensity of light times cosine square of the angle we have compute.

02:32 So, with this relation, we compute the intensity of the light that passed through a polarizer when the incident light has a special polarizing direction.

02:47 Well, this is just i0 over 2, and this is 1 half square...

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