Unpolarized light and Polarizers

[hellogirl88]

Unpolarized light propagating along the x-axis from the left in the image above encounters two polarizing filters in a row. The first filter is oriented with its polarization axis at θ1 = 80 degrees from the y-axis, and the second is oriented with its polarization axis at θ2 = 65 degrees from the y-axis. What is the final intensity of the light as a fraction of the original (pre-filter) intensity?

Ive tried doing this problem in every conceivable way possible and I can't get it right.

Please help! I know you have to use a variation of I2=I0*cos^2(theta1) *cos^2(theta2-theta1), but this isn't correct, so what am I doing wrong?

Thanks!

 

[Redbelly98]

Since the light is initially unpolarized, what is the effect of the first polarizer?

 

[nlightner]

I can understand your frustration with this problem. It is important to carefully consider the orientation of the polarizers and the angle of polarization in order to correctly calculate the final intensity of the light. Let's break down the problem step by step.

First, we know that unpolarized light consists of waves vibrating in all possible directions perpendicular to the direction of propagation. When this light encounters a polarizer, it only allows waves vibrating in a specific direction to pass through, blocking all others. So, the first polarizer with an orientation of θ1 = 80 degrees from the y-axis will only allow light waves vibrating at that angle to pass through.

Next, we have to consider the second polarizer with an orientation of θ2 = 65 degrees from the y-axis. This polarizer will only allow light waves vibrating at that angle to pass through, but since the light has already passed through the first polarizer, it will only allow light waves vibrating at an angle of 15 degrees (90 - 80) to pass through.

Now, we can use the formula for Malus' Law, which states that the final intensity (I2) is equal to the initial intensity (I0) multiplied by the cosine squared of the angle between the two polarizers (θ2 - θ1). In this case, that would be θ2 - θ1 = 15 degrees.

So, the final intensity (I2) as a fraction of the original intensity (I0) would be I2/I0 = cos^2(15) = 0.933. This means that the final intensity of the light would be approximately 93.3% of the original intensity.

I hope this helps clarify the problem and how to approach it. Remember to carefully consider the orientation and angle of polarization of the polarizers in order to correctly calculate the final intensity of the light. Keep practicing and don't get discouraged! Science is all about trial and error and learning from mistakes.