Unpolarized light passes through two Polaroid sheets. The transmission axis of the second polarizing filter makes an angle of 340 with the axis of the first polarizer. What fraction of the original unpolarized light is transmitted through the second polarizing filter?

This question is incomplete, the complete question is;

Unpolarized light passes through two Polaroid sheets. The transmission axis of the second polarizing filter makes an angle of 34° with the axis of the first polarizer. What fraction of the original unpolarized light is transmitted through the second polarizing filter?

the fraction of the original unpolarized light transmitted through the second polarizing filter is 0.343

Explanation:

We know that when Unpolarized light passes through first polarizer, it's intensity will be reduced to half  i.e

I1 = I0/2

Now after that when light passes through 2nd polarizer, Intensity will be;

I2 = I1 × (cos A1)²  

but  I1 = I0/2

so

I2 = (I0/2) × (cos A1)²

I2/I0 = 0.5 × (cos A1)²

In the question we were given that; The transmission axis of the second polarizing filter makes an angle of 34° with the axis of the first polarizer

so A = 34°

so we substitute

I2/I0 = 0.5 × (cos 34)²

I2/I0 = 0.343

Therefore the fraction of the original unpolarized light transmitted through the second polarizing filter is 0.343

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