A unpolarized electromagnetic wave is incident on a series of three straight polarizers, the 2nd with the polarization angle rotated at 30o and the third at 90o through respect to the an initial polarizer. If the initial intensity of the unpolarized light is I0, what is the soot I3 sent by the stack?

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Solution:

Concepts:PolarizationReasoning:For a polarized EM wave event on a polarizer, Itransmitted = I0cos2θ. Right here θ the angle between E0 and also the infection axis.Details the the calculation:After passing with the first polarizer, I1 = Io/2. ~ passing through the second polarizer I2 = I1 cos2(30o). Lastly after passing through the third polarizer, I3= I2 cos2(60o). Thus, I3 = Io cos2(30o)cos2(60o)/2 = 0.094 Io.Problem:

(a) i think the electric field that a plane wave propagating in the z-direction oscillates in the x-direction. What mix of polarizers would certainly transmit the beam so that would emerge with the electric field oscillating in the y-direction. Assume the perfect linear and circular polarizers room available. Perfect straight polarizers transmit 100% the the event wave in one aircraft of polarization and absorb 100% in the perpendicular plane. Circular polarizers (quarter-wave plates) retard one airplane of polarization ¼ wavelength relative to the perpendicular plane of polarization and hence can change a linearly polarized wave to a right- or left-hand circularly polarized wave and also vice versa, depending on the orientation of the direct polarization.(b) What combination of polarizers would readjust a right-hand circularly polarized beam travel in the z-direction right into a left-hand circularly polarized beam. How?

Solution:

Concepts:Polarization, linear and circular polarizersReasoning:We are supposed to find a mix of polarizers that turn the polarization axis through 90o.Details of the calculation:(a) E
= ε0cos(kz - ωt)i describes the EM wave before polarizers are inserted in its path.

You are watching: An unpolarized em wave is incident on two orthogonal polarizers.

Consider two coordinate equipment rotated about the z-axis 45o v respect come each various other as shown below.
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Insert direct polarizer v its transmission axis follow me x\" adhered to by a direct polarizer through its infection axis follow me y. After ~ the first polarizer we have E
= E0cos(45o)cos(kz - ωt + φ)i\",and after the 2nd polarizer us haveE = E0cos(45o)2cos(kz - ωt + φ)j.The amplitude the the tide is diminished by a aspect of 2 and also the strength by a variable of 4.To possibility the straight polarization without reducing the amplitude us use two quarter-wave plates. I think the quarter-wave bowl is oriented so the step of light polarized follow me x\" is retarded by π/2 v respect come the phase of light polarized along y\".Then we have before the platesEx\" = 2-½E0cos(kz - ωt),Ey\" = -2-½E0cos(kz - ωt).After one quarter-wave plate we haveEx\" = 2-½E0cos(kz - ωt + φ\"),Ey\" = -2-½E0cos(kz - ωt + φ\" + π/2).After 2 quarter-wave plates we haveEx\" = 2-½E0cos(kz - ωt + φ\"\"),Ey\" = -2-½E0cos(kz - ωt + φ\"\" + π) = 2-½E0cos(kz - ωt + φ\"\")E = E0cos(kz - ωt + φ\"\")j. The polarization has been rotated through 90o however the amplitude has actually remained the same.(c) Convention: once viewed looking in the direction of the source, a appropriate circularly polarized beam in ~ a fixed position as a role of time has actually a ar vector that describes a clockwise circle, if left circularly polarized light has a ar vector that explains a counter-clockwise circleRHC polarized light: Ex\" = E0cos(kz - ωt), Ey\" = E0sin(kz - ωt)LHC polarized light: Ex\" = E0cos(kz - ωt), Ey\" = -E0sin(kz- - ωt)After 2 quarter-wave key the ar of the RHC polarized wave becomesEx\" = E0cos(kz - ωt+φ), Ey\" = E0sin(kz - ωt + φ + π) = -E0sin(kz - ωt + φ). The tide becomes a LHC polarized wave.Problem:

(a) define how to prepare a monochromatic airplane wave of linearly polarized clearly shows light.(b) define how come prepare a monochromatic airplane wave of circularly polarized clearly shows light

Solution:

Concepts:Wavelength selection, polarization, linear and circular polarizersReasoning:Prisms or gratings space dispersive elements. Perfect linear polarizers transmit 100% the the incident wave in one plane of polarization and also absorb 100% in the perpendicular plane. One polarizers (quarter-wave plates) retard one plane of polarization ¼ wavelength relative to the perpendicular plane of polarization and hence can change a linearly polarized wave to a right- or left-hand circularly polarized wave and also vice versa, relying on the orientation the the direct polarization.Details that the calculation:(a) A airplane wave in handy applications is a tide front with a well-defined direction that of propagation, expanding over an area bigger than the cross-sectional area of an item to it is in illuminated.The figure listed below shows a possible method of prepare a linearly polarized plane wave.

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(b) The figure listed below shows a possible an approach of prepare a circularly polarized airplane wave.
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