Polarization and decreasing intensity of light to 10%

[aChordate]

Homework Statement

In order to decrease the intensity of a beam of unpolarized light to 10% of its original
intensity using two polarizers, what is the required value of θ, the angle between the
transmission axes of the two polarizers?

Homework Equations

tanθ_B=n₂/n₁

The Attempt at a Solution

tanθ_B=n₂/n₁

I'm not sure how to do this. I read the section on polarization and there are no examples in the book.

 

[Saitama]

Homework Statement

In order to decrease the intensity of a beam of unpolarized light to 10% of its original
intensity using two polarizers, what is the required value of θ, the angle between the
transmission axes of the two polarizers?

Homework Equations

tanθ_B=n₂/n₁

The Attempt at a Solution

tanθ_B=n₂/n₁

I'm not sure how to do this. I read the section on polarization and there are no examples in the book.

You seem to have mixed up Brewster's law with the Law of Malus. Check you textbook about the Law of Malus.

 

[aChordate]

So my equation would change to S=S_o=cos²θ

Would it be:

1/10*I=1/2*I*cos²θ ?


1/5=cos²θ

θ=63.4°

?

 

[Saitama]

So my equation would change to S=S_o=cos²θ

Would it be:

1/10*I=1/2*I*cos²θ ?


1/5=cos²θ

θ=63.4°

?

Looks good to me.

 

[Nickie]

I can provide some guidance on how to approach this problem. First, let's review the concept of polarization. Polarization is the process of restricting the vibrations of light to a single plane. This can be achieved by using a polarizer, which is a material that only allows light waves with a specific orientation to pass through.

Now, in order to decrease the intensity of a beam of unpolarized light to 10% of its original intensity, we need to use two polarizers. The first polarizer will polarize the light, and the second polarizer will further restrict the vibrations of the light to a single plane. This will result in a decrease in intensity.

The angle between the transmission axes of the two polarizers, θ, is important because it determines the amount of light that can pass through. The transmission axis of a polarizer is the direction in which the light can pass through. So, if the transmission axes of the two polarizers are parallel, then all of the light that passes through the first polarizer can also pass through the second polarizer. However, if the transmission axes are perpendicular, then no light can pass through the second polarizer.

In this problem, we are given that we want to decrease the intensity of the light to 10% of its original intensity. This means that only 10% of the light can pass through the second polarizer. So, we need to find the angle θ that will result in only 10% of the light passing through the second polarizer.

To do this, we can use the equation tanθB=n2/n1, where n1 is the index of refraction of the first polarizer and n2 is the index of refraction of the second polarizer. We can also substitute 10% for n2/n1, since we want to decrease the intensity to 10%.

So, our equation becomes tanθB=0.1. To solve for θ, we can use a scientific calculator to take the inverse tangent (tan^-1) of 0.1, which gives us an angle of approximately 5.71 degrees.

Therefore, the required value of θ, the angle between the transmission axes of the two polarizers, is approximately 5.71 degrees in order to decrease the intensity of the light to 10% of its original intensity.