PHY 2020 Lecture Notes - Lecture 41: Transverse Wave, Electric Field, Polarizer

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10 Feb 2020

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Polarization is the direction in which the electric field component (of electromagnetic wave) oscillates. Natural light (e. g. sun light) is randomly polarized in all directions. An electromagnetic wave is linearly polarized if the electric field has only one component. The effect of a polarizing filter on unpolarized incident light. The intensity of the transmitted light is the same for all orientations of the polarizing filter: for an ideal polarizing filter, the transmitted intensity is half the incident intensity. When unpolarized light is incident to the polarizer, the density ( average power per unit area) of transmitted light through the polarizer. Figure below shows a polarizer and an analyzer. Malus"s law: when linearly polarized light strikes a polarizing filter with its axis at an angle 0 to the direction of polarization, the intensity of the transmitted light. The linearly polarized light from the first polarizer can be resolved into component parallel and perpendicular respectively, to the polarizing axis of the analyzer.

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DUE DATE: 12 00 noon Monday. Dec 6. 2010. The problems on this assignment are quite word because strong direction is being given to Students in how to proceed. Two problems will be selected at random for marking. Percentage polarization. It is useful to characterize partially polarized light in terms of its "percentage polarization". A light beam of constant intensity Io. is allowed to fall at normal incidence on an "ideal linear polarizer" (a linear polarizer is "ideal" if it panes all light polarized parallel to the polarizer's axis, and stops all light polarized perpendicular to that axis.) As the ideal polarizer is rotated continuously (see Figure 8.1; about an axis perpendicular to its plane, the transmitted intensity I passes through successive maximum and minimum values (denoted by I max and I min). The percentage polarization of the incident light is denned to be Find the percentage polarization measured in this way for the following light beams: "Unpolarized natural light" tor which I max = I min = Io/2. A beam of light. Initially unpolarixed. that has been passed through an ideal linear polarizer before being measured for percentage polarization. A beam of light, initially unpolarizcd, that has been passed through a non-ideal polarizer that (in terms of light intensity) transmits 70% of light polarized parallel to its polarizing axis and 20% of light polarized perpendicular to its polarizing axis. Circularly polarized light. (Circular polarization means that at any given fixed observation point In the beam, the E-vector has constant magnitude but rotates at the frequency of the electric field oscillations so that the tip of the vector describes a circle in the zy plane (perpendicular to the light ray at the point in question). Elliptically polarized light for which the tip of the E-vector moves on an ellipse in the x y plane, defined by where Ax and Ay are the amplitudes of the oscillating Ex and E y components of the electric field vector, and is the phase difference between those oscillations. NOTE: Do your calculation for the special case Ax = 2Ay and e =pi / 2. [(8.2) taxes a particularly simple form when e = pi / 2.]

The light in Problem 62 travels toward a workbench and encounters two polarizing filters.

a. If the light passes first through a filter with its transmission axis at an angle of from the z direction, and then through a filter with its transmission axis at an angle of from the z direction, what is the final intensity of the transmitted light?

b. If, instead, the light passes first through a filter with its transmission axis at an angle of from the z direction, and then through a filter with its transmission axis at an angle of from the z direction, what is the final intensity of the transmitted light?

Problem 62:

Suppose you have a polarized light source in your lab that has an intensity of , where the electric field oscillates in the z direction. The light travels toward a workbench where you can send it through either one of two polarizing filters.

a. If the light passes through a filter with its transmission axis at an angle of from the z direction, what is the intensity of the transmitted light?

b. If, instead, the light passes through a filter with its transmission axis at an angle of 90.0° from the z direction, what is the intensity of the transmitted light?

yellowbeetle239

a. Is the light of the Sun Polarized?

b. The light emitted by the Sun is mostly yellow so that its wavelength is about 550 nm. What is its frequency?

c. The distance between the Earth and the Sun is about 149 million kilometers. How long does it take for the light to travel this distance?

d. A polarizer is placed in the xy-plane. Its polarization axis coincides with the x-axis. The z-axis is taken as the line of sight when looking at the Sun. What is the direction of the transmitted light electric field? What is the direction of the transmitted magnetic field? Sketch the direction of light propagation, the direction of the electric field, and the direction of the magnetic field of the transmitted light.

e. The intensity per unit we receive from the sun is about1413W/m^2. What is the intensity of the transmitted light after the polarizer?

f. If you could look only at the light after it had been reflected, say, by the sea (and NOT AT ALL at the direct radiation), what would you see?

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PHY 2020 Lecture Notes - Lecture 41: Transverse Wave, Electric Field, Polarizer

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