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12 May, 18:18

Unpolarized light of intensity i0 is incident on three polarizing filters. the axis of the first is vertical, that of the second is 43° from vertical, and that of the third is horizontal. what light intensity emerges from the third filter?

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  1. 12 May, 20:18
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    To determine the intensity, the key idea is to work through the system filter-by-filter and applying either the one-half rule for unpolarized light or the cosine-squared rule for an already polarized light.

    When the light reach the first filter, it is unpolarized, so the intensity is:

    I1 = 1/2 I0 (One-half rule)

    Because the light reaching the second filter is polarized, given 43° angle difference, the intensity is:

    I2 = I0 cos^2 (angle difference)

    = I0 cos^2 43°

    = 0.535 I0

    Lastly, when the light reached the third filter, it is polarized and has angle diference equals to the angle between the second and last filter 47°. Using the same rule, we get:

    I3 = I2 cos^2 47°

    = (0.535 I0) cos^2 47°

    = (0.535 I0) (0.465)

    = 0.249 I0

    So, the intensity which emerges is 0.249 I0.
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