In Figure P37.52, suppose the transmission axes of the left and right polarizing disks are perpendicular to each other. Also, let the center disk be rotated on the common axis with an angular speed ω. Show that if unpolarized light is incident on the left disk with an intensity Imax, the intensity of the beam emerging from the right disk is
This result means that the intensity of the emerging beam is modulated at a rate four times the rate of rotation of the center disk. Suggestion: Use the trigonometric identities
Figure P37.52
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Chapter 38 Solutions
Physics for Scientists and Engineers, Volume 1
- In Figure P37.52, suppose the transmission axes of the left and right polarizing disks are perpendicular to each other. Also, let the center disk be rotated on the common axis with an angular speed . Show that if unpolarized light is incident on the left disk with an intensity Imax, the intensity of the beam emerging from the right disk is I=116Imax(1cos4t) This result means that the intensity of the emerging beam is modulated at a rate four times the rate of rotation of the center disk. Suggestion: Use the trigonometric identities cos2=12(1+cos2) and sin2=12(1cos2). Figure P37.52arrow_forwardA linearly polarized microwave of wavelength 1.50 cm is directed along the positive x axis. The electric field vector has a maximum value of 175 V/m and vibrates in the xy plane. Assuming the magnetic field component of the wave can be written in the form B = Bmax sin (kx t), give values for (a) Bmax, (b) k, and (c) . (d) Determine in which plane the magnetic field vector vibrates. (e) Calculate the average value of the Poynting vector for this wave. (f) If this wave were directed at normal incidence onto a perfectly reflecting sheet, what radiation pressure would it exert? (g) What acceleration would be imparted to a 500-g sheet (perfectly reflecting and at normal incidence) with dimensions of 1.00 m 0.750 m?arrow_forwardFigure P24.13 shows a plane electromagnetic sinusoidal wave propagating in the x direction. Suppose the wavelength is 50.0 m and the electric field vibrates in the xy plane with an amplitude of 22.0 V/m. Calculate (a) the frequency of the wave and (b) the magnetic field B when the electric field has its maximum value in the negative y direction. (c) Write an expression for B with the correct unit vector, with numerical values for Bmax, k, and , and with its magnitude in the form B=Bmaxcos(kxt) Figure P24.13 Problems 13 and 64.arrow_forward
- In the figure, the orientation of the transmission axis for each of three polarizing sheets is labeled relative to the vertical direction. A beam of unpolarized light is incident on the first polarized with an intensity of lo. The final intensity of the beam of light is 0.251, after it has passed through the three polarizing sheets. What is the value of 03 if 0q= 15°, 02 = 50°?arrow_forwardThree polarizing disks whose planes are parallel and centred on common axis. The directions of their transmission axes relative to the vertical are respectively: θ1 = 38o clockwise, θ2 = 25o counter-clockwise, and θ3 = 12o clockwise. A beam of light polarized along the vertical is incident onto the first polarizer with an intensity of I0 = 24.0 W/m². Calculate the transmitted intensity through all three polarizers.arrow_forwardProblem 1: a. Determine the polarization state of a plane EM wave with electric field E = 3 sin (ot – Bz +30°) a; + 4 cos (@t – Bz +45°) ay b. Prove that a plane linearly polarized wave can be resolved into two circularly polarized wave traveling in the same direction but with opposite polarization orientations.arrow_forward
- The orientation of the transmission axis for three polarizing sheets is labeled relative to the vertical direction. A beam of light, polarized in the vertical direction, is incident on the first polarized with an intensity of Ii. The final intensity of the beam of light is half of the original intensity after it has passed through the three polarizing sheets . What is the value of θ3 if θ1= 10°, θ2 = 40°?arrow_forwardAn unpolarized beam of light (intensity I0) is moving in the x-direction. The light passes through three ideal polarizers whose transmission axes are (in order) at angles 0.0°, 48.0°, and 22.0° counterclockwise from the y-axis in the yz-plane. If the polarizer in the middle is removed, what is the intensity and polarization of the light transmitted by the last polarizer?arrow_forwardA beam of initially unpolarized light passes through a sequence of three ideal polarizers. The angle p12 between the axes of the first and second polarizers is 23.9°, and the angle ø23 between the axes of the second and third polarizers is 58.7°. P12 P23 What is the ratio of the intensity I3 of light emerging from the third polarizer to the intensity Io of light incident on the first polarizer? I3 Ioarrow_forward
- If a light beam of intensity I0 that is linearly polarized along the +z-axis is incident on P1, what is the intensity of the transmitted light after it passes through all the polarizers?arrow_forwardJ W E 10. Three polarizing disks have planes that are parallel and centered on a common axis. The direction of the transmission axis (dashed line) in each case is shown relative to the common vertical direction. A polarized beam of light (with its axis of polarization parallel to the horizontal reference direction) is incident from the left on the first disk with intensity S, = 820 W/m2. Calculate the transmitted intensity if 0₁ = 21.0°, 0₂ = 34.0°, and 03 = 44.0°. X 658.06 W/m² R 92 5 T 6 Horizontal MacBook Air U 8 61arrow_forwardUnpolarized light is sent into a system of three polarizing sheets. The angles θ1, θ2, and θ3 of the polarizing directions is measured counterclockwise from the positive direction of the y axis. Angles θ1 and θ3 are fixed, but angle θ2 can be varied. The figure gives the intensity of the light emerging from sheet 3 as a function of θ2. (a) From the intensity plot, what are the possible orientations of the first and third polarizers? Draw a sketch of the situation. (b) What percentage of the light’s initial intensity is transmitted by the three-sheet system when θ2 = 90°? Answer: 7.3%arrow_forward
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