Question

The angle between the axes of two polarizing filters is 45.0^\circ45.0 ​∘ ​​ . By how much does the second filter reduce the intensity of the light coming through the first? Select the correct answer 0.750 0.800 0.250 0.500 Your Answer 0.125 Saved 1 of 3 attempts used Part b (1 points) What now is the direction of polarization of the transmitted light? (You can assume the first polarizer defines the angle \theta = 0θ=0.) Select the correct answer

Answer 1

The second filter reduces the intensity of the light coming through the first by a factor of 0.5 and the transmitted light is polarised at an angle of  45° from the horizontal.

Let us assume that the initial intensity of unpolarized light be I₀.

When the light passes through the first polarizer the intensity becomes:

$I=I_0$

where θ varies from 0 to 2π, so <cos²θ> = 1/2

therefore, $I=I_0/2$

Now the light is passed through a second polarizer at an angle of 45°, its intensity becomes:

$I'=Icos^245^o\\\\I'/I=cos^245^o\\\\I'/I=1/2=0.5$

so the light coming out of the first polarizer gets reduced in intensity by a factor of 0.5 and the transmitted light is polarised at an angle of  45° from the horizontal.

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