University Physics Volume 3
17th Edition
ISBN: 9781938168185
Author: William Moebs, Jeff Sanny
Publisher: OpenStax
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Textbook Question
Chapter 1, Problem 67P
What angle would the axis of a polarizing filter need to make with the direction of polarized light of intensity
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Unpolarized light of intensity 20.0 W/cm2 is incident on two polarizing filters. The axis of the first filter is at an angle of 25.0° counterclockwise from the vertical (viewed in the direction the light is traveling), and the axis of the second filter is at 62.0° counterclockwise from the vertical. What is the intensity of the light after it has passed through the second polarizer?
A polarizer reduces the intensity of light by a factor of 0.5. At what angle should the analyzer be oriented so the average intensity of light leaving the analyzer is reduced to 0.10?
Some unpolarized light has an intensity of 1315 W/m2 before passing through three polarizing filters. The transmission axis of the first filter is vertical. The second filter's transmission axis is 24.0° from vertical. The third filter's transmission axis is 38.0° from vertical. What is the intensity of the light that emerges from the three filters?
Chapter 1 Solutions
University Physics Volume 3
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- An unpolarized beam of light is incident on a stack of ideal polarizing filters. The axis of the first filter is perpendicular to the axis of the last filter in the stack. Find the fraction by which the transmitted beams intensity is reduced in the three following cases. (a) Three filters are in the stack, each with its transmission axis at 45.0 relative to the preceding filter. (b) Four filters are in the stack, each with its transmission axis at 30.0 relative to the preceding filter. (c) Seven filters are in the stack, each with its transmission axis at 15.0 relative to the preceding filter. (d) Comment on comparing the answers to parts (a), (b), and (c).arrow_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_forwardIn 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_forward
- If a polarizing filter reduces the intensity of polarized light to 50.0% of its original value, by how much are the electric and magnetic fields reduced?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_forwardWhat angle is needed between the direction of polarized light and the axis of a polarizing filter to cut its intensity in half?arrow_forward
- The Poynting vector describes a flow of energy whenever electric and magnetic fields are present. Consider a long cylindrical wire of radius r with a current I in the wire, with resistance R and voltage V. From the expressions for the electric field along the wire and the magnetic field around the wire, obtain the magnitude and direction of the Poynting vector at the surface. Show that it accounts for an energy flow into the wire from the fields around it that accounts for the Ohmic heating of the wire.arrow_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_forwardUnpolarized light in vacuum is incident onto a sheet of glass with index of refraction n. The reflected and refracted rays are perpendicular to each other. Find the angle of incidence. This angle is called Brewsters angle or the polarizing angle. In this situation, the reflected light is linearly polarized, with its electric field restricted to be perpendicular to the plane containing the rays and the normal.arrow_forward
- Unpolarized light passes through three polarizing filters. The first filter has it transmission axis parallel to the z direction, the second has its transmission axis at an angle of 30 degrees from the z direction, the third has its transmission axis at an angle of 60 degrees from the z direction. If the light that emerges from the third filter has an intensity of 36.0 W/m2, what is the original intensity of the light? (Assume both angles are measured in the same direction from the +z axis). Use cos(30)=√3/2.arrow_forwardA beam of light with an intensity of 40.0 W/m2 and polarization parallel to the y-axis is sent into a system of two polarizing filters with transmission axes of 01 = 70.0° and 02 = 90.0° with respect to the y-axis. What is the intensity of the light transmitted by the two-filter system? y O 4.13 W/m2 O 2.88 W/m2 O 3.29 W/m2 O 3.82 W/m? O 4.63 W /m?arrow_forwardUnpolarized light with intensity 350 W/m² passes first through a polarizing filter with its axis vertical, then through a second polarizing filter. It emerges from the second filter with intensity 131 W/m². What is the angle from vertical of the axis of the second polarizing filter?arrow_forward
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Polarization of Light: circularly polarized, linearly polarized, unpolarized light.; Author: Physics Videos by Eugene Khutoryansky;https://www.youtube.com/watch?v=8YkfEft4p-w;License: Standard YouTube License, CC-BY