The drawing shows four sheets of polarizing material, each...

The drawing shows four sheets of polarizing material, each with its transmission axis oriented differently. Light that is polarized in the vertical direction is incident from the left and has an average intensity of 27 $W /m^{2}$. Determine the average intensity of the light that emerges on the right in the drawing when sheet A alone is removed, when sheet B alone is removed, when sheet C alone is removed, and when sheet D alone is removed.

Key Concepts

Polarization of Light

This concept refers to the orientation of the electric field vector in a light wave. Light can be polarized in various directions, and understanding its polarization is essential when analyzing how light interacts with optical elements like polarizing filters.

Polarizing Filters

Polarizing filters are optical elements that permit light waves with a specific polarization direction to pass through while blocking waves with other orientations. Their key function is to control the state of polarization in a beam of light, often used in applications ranging from glare reduction to optical experiments.

Transmission Axis

The transmission axis of a polarizing filter is the specific direction along which light is allowed to pass. The orientation of this axis is crucial, as it determines which component of the light's electric field is transmitted, thereby directly influencing the intensity and polarization state of the emerging light.

Malus's Law

Malus's Law mathematically describes how the intensity of polarized light changes as it passes through a polarizing filter. According to this law, if the angle between the light's polarization direction and the filter's transmission axis is ?, the transmitted intensity is proportional to the square of the cosine of this angle, a principle that is fundamental when analyzing light behavior in systems with multiple polarizers.

Transcript

00:01 Hello everyone.

00:02 This is going to be the solution to problem 48 of chapter 24 of cognol's physics.

00:07 We are presented with a scenario where we have four polarizers in a row, and we're taking them out one by one and seeing what the emergent intensity on the far right of all the polarizers is going to be.

00:24 So first scenario, we would normally have a vertical polarizer here, but that's what we've removed.

00:30 So removing that, we have a vertically polarized right coming in.

00:39 And so let me just write what the end polarization is going to be, what the end intensity is going to be.

00:47 It's going to be the initial intensity times.

00:54 So this is a cross -section of what's happening here.

00:57 We have a polarized light at the word.

01:01 Direction that is making an angle 30 degrees with the direction of the polarization that's going out with the polarization axis of the polarizer.

01:13 So projecting this polarization onto the polarization axis through the angle 30 degrees, we get that this is going to reduce our intensity by cost squared of 30 degrees.

01:27 Moving into the second part, we have this intensity coming into the second polarizer, and this has a polarization axis that is horizontal.

01:38 Now, we have been polarized at 30 degrees with respect to the vertical direction, which means that our current polarization is making a 60 degree angle with the horizontal.

01:51 And so we need to project through this angle onto the polarization axis, which means that we're going to pick up another factor of cost squared 60 degrees this next.

02:02 Time.

02:04 And so this is the result of intensity that's coming on to the third and last polarizer, where we see that we had been polarized horizontally, and this new polarization axis makes an angle of 60 degrees with the vertical, which means that this angle is 60 degrees.

02:26 This angle here is 60 degrees.

02:29 So that means that our current polarization is going to be making a 30 degree angle with the new polarization axis.

02:37 And so we're going to pick up an other factor of cost squared of 30 degrees.

02:43 And so this is going to be the result of intensity coming out on a far right.

02:49 And for an incident intensity of 27 watts per meter squared, this is going to work out to be 3 .8 watts per meter squared.

03:04 So that's the answer to your first part.

03:07 Second part, now i imagine that we had kept the vertical polarizer, but we had removed the 30 degree polarizer, which means that the next polarizer after the vertical one is going to be horizontal one.

03:24 So this means that our the light polarized that parallel to the vertical axis is going to come on to the polarizer that has a particular axis is going to come on to the polarizer that has a polarization axis that is horizontal...

Please give Ace some feedback