3/31/2014 Master Ithttp://www.webassign.net/v4cgi/questions/tutorial_popup.tpl 1/2Master ItPlanepolarized light is incident on a single polarizing disk with the direction of parallel to the direction ofthe transmission axis. Through what angle should the disk be rotated so that the intensity in the transmittedbeam is reduced by a factor of:(a) 2.10(b) 6.10(c) 10.5Part 1 of 5 ConceptualizeMaximum intensity is transmitted by the polarizing disk analyzer when its axis is at to the polarizationdirection of the incident light. Turning the disk more and more, approaching will decrease thetransmitted intensity by larger and larger factors.Part 2 of 5 CategorizeWe will use the equation known as Malus's law for the intensity of light transmitted through the polarizingmaterial.Part 3 of 5 AnalyzeWe define the initial angle at which all the light is transmitted to be θ = 0. Turning the disk to another anglewill reduce the transmitted light by an intensity factor described by Malus's lawSolving for θ, we obtain the following.(a) For we havePart 4 of 5 Analyze(b) For we have0E0°90°,I = Imax cos2 θ.θ = cos−1IImax1/2 I = Imax/2.10,θ = cos−1 = cos−1 = cos−1 0.69 = 46.4 °.IImax1/2 1 2.1I = Imax/6.10,θ = cos−1 = cos−1 = cos−1 0.405 = 66.1 °.IImax1/2 1 6.13/31/2014 Master Ithttp://www.webassign.net/v4cgi/questions/tutorial_popup.tpl 2/2Part 5 of 5 Analyze(c) For we haveThe largest factor of intensity reduction requires the largest crossing angle.FinalizeThe cosine in Malus's law takes the component of the incident electric field to be along the direction of thetransmission axis of the polarizing filter. This factor is squared because the energy of any oscillator isproportional to the square of its amplitude. The intensity of any traveling wave is also proportional to thesquare of its amplitude.I = Imax/10.5,θ = cos−1 = cos−1 = cos−1 0.309 = 72 °.IImax1/2 1
View Full Document
Unlocking...