Optical Polarizers in Series

The following problems deal with polarizers, which is a device used to alter the polarization of an optical wave.

  1. Unpolarized light of intensity I is incident on an ideal linear polarizer (no absorption). What is the transmitted intensity?

    Unpolarized light contains all possible angles to the linear polarizer. On a two dimensional plane, the linear polarizer will emit only that amount of light intensity that is found in the axis of polarization. Therefore, the Intensity of light emitted from a linear polarizer from incident unpolarized light will be half the intensity of the incident light.

  2. Four ideal linear polarizers are placed in a row with the polarizing axes vertical, 20 degrees to vertical, 55 degrees to vertical, and 90 degrees to vertical. Natural light of intensity I is incident on the first polarizer.

    a) Calculate the intensity of light emerging from the last polarizer.

    b) Is it possible to reduce the intensity of transmitted light (while maintaining some light transmission) by removing one of the polarizers?

    c) Is it possible to reduce the intensity of transmitted light to zero by removing a polarizer(s)?

    a) Using Malus’s Law, the intensity of light from a polarizer is equal to the incident intensity multiplied by the cosine squared of the angle between the incident light and the polarizer. This formula is used in subsequent calculations (below). The intensity of light from the last polarizer is 19.8% of the incident light intensity.

    b) My removing polarizer three, the total intensity is reduced to 0.0516 times the incident intensity.

    c) In order to achieve an intensity of zero on the output of the polarizer, there will need to exist an angle difference of 90 degrees between two of the polarizers. This is not achievable by removing only one of the polarizers, however it would be possible by removing both the second and third polarizer, leaving a difference of 90 degrees between two polarizers.

 

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