32. Electromagnetic Waves

FIGURE EX31.23 shows a horizontally polarized radio wave of frequency 1.0×10⁶ Hz traveling into the figure. The maximum electric field strength is 1000 V/m. What is the maximum magnetic field strength?

Horizontallypolarized lightis incident ona polarization filter. The initial intensity of the light is 0.55 W/m², but is then reduced to 0.40W/m²after passing through the filter. Calculate the angle of the transmission axis of the polarization filter with respect to the horizontal.

(II) Two polarizers A and B are aligned so that their transmission axes are vertical and horizontal, respectively. A third polarizer is placed between these two with its axis aligned at angle θ with respect to the vertical. Assuming vertically polarized light of intensity I₀ is incident upon polarizer A, find an expression for the light intensity I transmitted through this three-polarizer sequence. Calculate the derivative dI / dθ ; then use it to find the angle θ that maximizes I.

Unpolarized light of intensity I₀ passes through six successive Polaroid sheets each of whose axis makes a 38° angle with the previous one. What is the intensity of the transmitted beam?

Light of original intensity I₀ passes through two ideal polarizing filters having their polarizing axes oriented as shown in Fig. E33.28. You want to adjust the angle f so that the intensity at point P is equal to I₀/10. If the original light is linearly polarized in the same direction as the polarizing axis of the first polarizer the light reaches, what should Φ be?

In each of the following cases, initially vertically polarized light enters the polarizing apparatus with the same initial intensity. Which polarizing apparatuses will cause the light to exit with the largest intensity, 90° from its initial polarization? 

a) A single polarizing filter, oriented 90° from the vertical 

b) Two polarizing filters, the first 45° from the vertical and the second 90° from the vertical 

c) Two polarizing filters, the first 60° from the vertical and the second 90° from the vertical 

d) Two polarizing filters, the first 30° from the vertical and the second 90° from the vertical.

Light of original intensity I₀ passes through two ideal polarizing filters having their polarizing axes oriented as shown in Fig. E33.28. You want to adjust the angle f so that the intensity at point P is equal to I₀/10. If the original light is unpolarized, what should Φ be?