Show that if you have three polarizing filters, with the second at an angle of 45 degrees to the first and the third at an angle of 90 degr

Question

Show that if you have three polarizing filters, with the second at an angle of 45 degrees to the first and the third at an angle of 90 degrees to the first, the intensity of light passed by the first will be reduced to 25% of its value. (This is in contrast to having only the first and third, which reduces the intensity to zero, so that placing the second between them increases the intensity of the transmitted light.)

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Verity 5 months 2021-08-11T11:27:07+00:00 1 Answers 69 views 0

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    2021-08-11T11:28:30+00:00

    Answer:

      I₃ /I₀ = 25%

    Explanation:

    For this exercise let’s use Malus’s law

             I = I₀ cos² θ

    where tea is the angle between the two polarizers.

    When the polarized light passes the first polarizer, the intensity is constant if it is in the direction of polarization.

            I₁ = I₀

    the light transmitted by the second polarizer is

            I₂ = I₁ cos² θ

            I₂ = I₀ cos² 45

            I₂ = I₀ 0.5

    this light is polarized 45º with respect to the first polarizer

    Now let’s examine the third polarizer, it is indicated that it has an angle of 90º with respect to the first polarizer, the angle with respect to the second polarizer is

            θ = 90 – 45

            θ = 45º

    so the polarizer is at an angle of 45º

    let’s use Maus’s law

             I₃ = I₂ cos² 45

             I₃ = I₀ 0.5 cos² 45

             I₃ = I₀ 0.25

    the light that passes through the system is

             I₃ /I₀ = 0.25

    as a percentage we multiply by 100

             I₃ /I₀ = 25%

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