Conceptual Physics (12th Edition)

Published by Addison-Wesley

Chapter 29 - Think and Discuss: 68

Answer

The inserted Polaroid changes the plane of the polarized light, letting some of it get through the final Polaroid filter.

Work Step by Step

Call the Polaroids 1, 2, and 3, in the order in which light encounters them. Say that filter #1 has a vertical polarization axis and #3 has a horizontal one. Filter #1 polarizes the incoming unpolarized light, letting half of it through, which now has a vertical polarization direction. This direction is perpendicular to the axis of filter #3. When these are the only filters present, no light gets through. However, when filter #2 is placed between 1 and 3, oriented diagonally, it is illuminated by polarized light that is aligned at $45^{\circ}$ to its own axis. It lets half of the light through, and polarizes it with a diagonal direction of polarization. The light illuminating filter #3 is now also aligned at $45^{\circ}$ to its own axis. So filter #3 also transmits half of the light that strikes it, which is one-eighth the intensity of the initially unpolarized light that illuminated filter #1. For more on this, look up the "Law of Malus" for polarizing filters. This is discussed on pages 555-556, and an analogy with ropes passing through a pair of picket fences is shown in Figure 29.32. This problem is discussed in the caption to Figure 29.34 and the answer is in Appendix D.

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