Two polarizing sheets have their transmission axes crossed so that no light gets through. A third...

Two polarizing sheets have their transmission axes crossed so that no light gets through. A third sheet is inserted between the first two so that its transmission axis makes an angle ? with the transmission axis of the first sheet. Unpolarized light of intensity I₀ is incident on the first sheet. Suppose that the middle sheet is replaced by two polarizing sheets. The angles between the transmission axes of the second, third and fourth sheets in the stack make angles of 30

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Look at this link, It's has a good picture of the transmission going on and makes more sense. I think when you make your calculation you may have to make the second cosine at cos 60 , ( 90deg-30deg) after the transmission thru the middle sheet because from the last sheet's perspective the light has already twisted 30 deg and is entering a sheet that is 90 degrees from the first sheet.

I'm not comfortable with the equation you used. Try using the one on the hyperphysics link.
It's called the law of Mathus. If you plug in 30 for the

first transmission thru the second sheet you get .8078.

If you take this .8078

transmission thru the 3rd sheet at 60 degrees you get a transmission of .1922.

Multiply the two and you get a total transmission of .1552.

I think you have to get the light transmission amount thru the second sheet and then plug in that amount in the equation and at the angle of 60 degrees to get the final transmission

This would make more sense, since no light was transmitted before the second sheet was inserted. This is the principle of polarized sunglasses. The angle of the 2nd sheet controls the shade or light transmission of the sunglasses

So I think your answer of .326 has to be way to much as that implies 32.6% of the light was transmitted thru all 3 sheets.

genius_generous answered 1 year ago

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