Unpolarized light of intensity 0.5 W/m^2 passes through a vertical polarizing fi

Question

Unpolarized light of intensity 0.5 W/m^2 passes through a vertical polarizing filter. The light then passes through a second polarizer whose axis 45 degree from the vertical. The light then passes through a third polarizer whose axis is horizontal. What is the intensity of the transmitted light after passing through the horizontal polarizer? Assume that the polarizers are close enough to each other that the light's intensity changes only when passing through a polarizer and not as it travels between them.

Explanation / Answer

Suppose initial intensity is I0

After the first polarizer intensity will be half

I1 = I0/2

After the second polarizer

I2 = I1*cos^2(phi)

I2 = I1*(cos 45 deg)^2

I2 = (I0/2)*(1/sqrt 2)^2

I2 = I0/4

After the third polarizer

I3 = I2*(cos 45 deg)^2

I3 = (I0/4)*(1/sqrt 2)^2

I3 = I0/8

I3 = 0.5/8 = 0.0625 W/m^2

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