Describe how to rotate the plane of polarization of a plane-polarized beam of light by 90° and produce only a 10% loss in intensity, using polarizers. Let N be the number of polarizers and θ be the (same) angle between successive polarizers.

At what angle should the axes of two Polaroids be placed so as to reduce the intensity of the incident unpolarized light by an additional factor (after the first Polaroid cuts it in half) of (a) 4, (b) 10, (c) 100?

A radio telescope, whose two antennas are separated by 55 m, is designed to receive 3.0-MHz radio waves produced by astronomical objects. The received radio waves create 3.0-MHz electronic signals in the telescope’s left and right antennas. These signals then travel by equal-length cables to a centrally located amplifier, where they are added together. The telescope can be “pointed” to a certain region of the sky by adding the instantaneous signal from the right antenna to a “time-delayed” signal received by the left antenna a time ∆t ago. (This time delay of the left signal can be easily accomplished with the proper electronic circuit.) If a radio astronomer wishes to “view” radio signals arriving from an object oriented at a 12° angle to the vertical as in Fig. 34–54, what time delay ∆t is necessary?

Two polarizers are oriented at 55° to each other and plane-polarized light is incident on them. If only 25% of the light gets through both of them, what was the initial polarization direction of the incident light?

"Two identical sources S₁ and S₂, separated by distance d, coherently emit light of wavelength λ uniformly in all directions. Defining the x axis with its origin at S₁ as shown in Fig. 34–52, find the locations (expressed as multiples of λ ) where the signals from the two sources are out of phase along this axis for x > 0 , if d = 3λ.