Unpolarized light passes through six successive Polaroid sheets each of whose axis makes a 59 degree angle with the previous one.

What is the intensity of the transmitted beam, I/Io?

After the light passes through the first Polaroid, it's intensity is 1/2Io. Now the light is polarized

After the second sheet, it is now

1/2I0*((cos(59))^2)

After the third sheet it is

1/2I0*((cos(59))^2)*((cos(59))^2)
. .

Do this up to the 6th sheet, and divide by I0

Well, let me just say this question is a bright one! So, you have unpolarized light passing through six Polaroid sheets, and they're all a little bit twisted from each other. It's like watching a dance where everyone is doing their own thing!

Now, when unpolarized light goes through a Polaroid sheet, it becomes polarized in the direction of the sheet's axis. So each time the light passes through a sheet, it gets more and more aligned with that sheet's axis, which, in this case, is twisted 59 degrees from the previous one. They're like synchronized swimmers, all going in the same direction but at slightly different angles.

Now let's address the elephant in the room - the intensity of the transmitted beam. The intensity of light is directly related to its polarization. If the light is completely aligned with the axis, the intensity will be maximum. If it's perpendicular, the intensity will be minimum.

In this case, since the light passing through each sheet is a little bit twisted, the intensity will decrease with each sheet. In fact, the intensity of the transmitted beam, I/Io, will be given by the equation:

I/Io = cos^2(theta)^n

Where theta is the angle between the axes of the sheets (in this case, 59 degrees), and n is the number of sheets (in this case, 6).

So, using this equation, go ahead and do some math, and you'll find the intensity of the transmitted beam, I/Io. But hey, don't let all these polarized sheets make your head spin! It's all about angles and intensity, just like a good magic trick. Enjoy your calculations!

To find the intensity of the transmitted beam, I/Io, we need to consider the Malus' Law.

Malus' law states that the intensity of light transmitted through a polarizer is given by the equation I = I0 * cos^2(θ), where I is the transmitted intensity, I0 is the initial intensity, and θ is the angle between the transmission axis of the polarizer and the plane of polarization of the incident light.

In this case, the initial angle between the first polarizer and the unpolarized light is not given, so let's assume it is 0 degrees.

Given: θ = 59 degrees for each successive polarizer.

To find the overall intensity of the transmitted beam after passing through six successive polarizers, we can use the equation:
I/I0 = cos^2(θ1) * cos^2(θ2) * ... * cos^2(θ6)

Substituting θ = 59 degrees, we have:

I/I0 = cos^2(59) * cos^2(59) * cos^2(59) * cos^2(59) * cos^2(59) * cos^2(59)

Using a scientific calculator, we can calculate the value:

I/I0 ≈ 0.0089

Therefore, the intensity of the transmitted beam, I/I0, is approximately 0.0089.

To find the intensity of the transmitted beam, I/Io, you need to understand the concept of Malus's law and how it applies to the transmission of polarized light through multiple Polaroid sheets.

Malus's law states that the intensity of polarized light transmitted through a Polaroid sheet is given by the equation:

I = Io * cos^2(θ),

where I is the intensity of the transmitted light, Io is the initial intensity of the incident light, and θ is the angle between the transmission axis of the Polaroid sheet and the polarization direction of the incident light.

In this case, each successive Polaroid sheet is rotated by an angle of 59 degrees from the previous one. To calculate the overall intensity of the transmitted beam through the six Polaroid sheets, you need to calculate the intensity for each sheet and then multiply them together.

Let's denote the intensity after passing through the first Polaroid sheet as I1, the intensity after passing through the second sheet as I2, and so on. The intensity after passing through all six sheets would be denoted as I6.

Using Malus's law, we can calculate the intensity after passing through each sheet:

I1 = Io * cos^2(0°)
= Io * 1
= Io

I2 = I1 * cos^2(59°)

I3 = I2 * cos^2(59°)

I4 = I3 * cos^2(59°)

I5 = I4 * cos^2(59°)

I6 = I5 * cos^2(59°)

To find the overall intensity of the transmitted beam, I/Io, we divide the final intensity (I6) by the initial intensity (Io):

I/Io = I6 / Io

Now, you can substitute the expressions for each intensity value and calculate the final result.

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