Three polarizing filters are stacked, with the polarizing axis of the second and

Question

Three polarizing filters are stacked, with the polarizing axis of the second and third filters at angles of 30.0 and 62.0 , respectively, to that of the first. If unpolarized light is incident on the stack, the light has an intensity of 72.0 W/cm2 after it passes through the stack.

Part A

If the incident intensity is kept constant, what is the intensity of the light after it has passed through the stack if the second polarizer is removed?

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Three polarizing filters are stacked, with the polarizing axis of the second and third filters at angles of 30.0 and 62.0 , respectively, to that of the first. If unpolarized light is incident on the stack, the light has an intensity of 72.0 W/cm2 after it passes through the stack.

Part A

If the incident intensity is kept constant, what is the intensity of the light after it has passed through the stack if the second polarizer is removed?

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Explanation / Answer

Here's the formula you'll be using for this problem: malus's law

I = Icos^2(theta)

When a ray goes through an ideal polarizer it gets cut in half. So you know that when the unpolarized light goes thorough the first polarizer it will be :

I = I/2 , let's call this I(1) for now.

Now you have the light travel through a second polarizer. The intensity of this light is now:

I = I(1)cos^2(30). We'll call this I(2)

Finally the light will travel past the third polarizer, and the intensity will be given by this:

I = I(2)cos^2(62-30). We'll Call this I(3)

You are given I(3) so what you have to do is solve for I2 and I1 backwards starting from I3.

72 = I2cos^2(62-30) = (I2 = 72/cos^2(62-30)) = 143.80

143.80 = I1cos^2(29) = (I1 = 143.80/cos^2(29)) = 187.98

So 187.98 is the intensity of the light after it passes through the first polarizer. Since the second one is removed , leaving the third one to do the rest of the light blocking, all you have to do is take the intensity of light after the first polarizer, and use Malus's law to calculate the new intensity with 3rd polarizer's angle.

Inew = 187.98cos^2(58) = 52.3

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