Physics help polarization

Question

Unpolarized light with an intensity of 22.4 lux passes through a polarizer whose transmission axis is vertically oriented. (a) What is the direction of polarized beam and intensity of the transmitted light? (b) If the polarizer’s transmission axis is at an angle of 69.0° with the vertical, what is the intensity of the transmitted light and its direction?

Answer 1

Polarized light is most commonly obtained by use of a material that transmits waves whose electric field vectors vibrate in a plane parallel to a certain direction and absorbs those waves whose electric field vectors vibrate in other directions. A dichroic substance transmits light with the electric field vibrating in only one direction. Polaroid, discovered in 1938, was found to polarize light through selective absorption by oriented molecules and is fabricated in thin sheets of long-chain hydrocarbons like polyvinyl alcohol. These sheets are stretched in their creation for alignment of the long-chain molecules. Dipping the sheets in an iodine solution renders the molecules conductive, but the conduction occurs primarily along the hydrocarbon chains since the valence electrons of the molecules move with ease only along the chains (since valence electrons are "free" electrons that readily move through the conductor).

The molecules then readily absorb light waves whose electric field vectors are perpendicular to their lengths. The direction perpendicular to the molecular chains is the transmission axis. In an ideal polarizer, all light with E parallel to the transmission axis is transmitted and all light with E perpendicular to the transmission axis is absorbed. Unpolarized light passing through a primary polarizing sheet (polarizer) with its transmission axis drawn on the sheet as a straight line will be polarized vertically; the transmitted electric field vector is E_0. A secondary polarizing sheet (analyzer) intercepts this beam with its transmission axis at angle θ to the axis of the polarizer.

The component of E₀ perpendicular to the axis of the analyzer is completely absorbed, and the component of E₀ parallel to the axis of the analyzer is E₀cosθ. Since the transmitted intensity varies as the square of the transmitted amplitude, it follows that I = I₀cos²θ with I₀ being the intensity of the polarized wave incident on the analyzer. I = I₀cos²θ (or Malus' Law) applies to any two polarizing materials whose transmission axes are at angle θ to each other. Note from Malus' Law that transmitted intensity is maximum when the transmission axes are parallel (θ = 0° or θ = 180°). Moreover, the transmitted intensity is 0 (complete absorption by the analyzer) when the transmission axes are perpendicular.

Then obtain I_v = 22.4cos²0° for a vertical transmission axis or I_v = 22.4 lux.

I_{69 Degrees} is then given by 22.4cos²69° equivalent to 2.9 lux.