Question
Recall that electromagnetic waves, such as visible light,microwaves, and X rays, consist of oscillating electric andmagnetic fields. The polarization of an electromagnetic wave refersto the oscillation direction of the electric field, not themagnetic field. In this problem all figures depicting light wavesillustrate only the electric field.
The two transverse waves shown in the figure (Intro1 Figure) both travel in the +z direction. Thewaves differ in that the top wave oscillates horizontally and thebottom wave oscillates vertically. The direction of oscillation ofa wave is called the polarization of the wave. The upperwave is described as polarized in the +x direction whereasthe lower wave is polarized in the +y direction. Ingeneral, waves can be polarized along any direction. Recall that electromagnetic waves, such as visible light,microwaves, and X rays, consist of oscillating electric andmagnetic fields. The polarization of an electromagnetic wave refersto the oscillation direction of the electric field, not themagnetic field. In this problem all figures depicting light wavesillustrate only the electric field. A linear polarizing filter, often just called a polarizer, is adevice that only transmits light polarized along a specifictransmission axis direction. The amount of light that passesthrough a filter is quantified in terms of its intensity. If thepolarization angle of the incident light matches the transmissionaxis of the polarizer, 100percent of the light will pass through, so thetransmitted intensity will equal the incident intensity. Moregenerally, the intensity of light emerging from a polarizer isdescribed by Malus^'s law: I = I_0cos^2 theta, where I_0 is the intensity of the polarized lightbeam just before entering the polarizer, I is the intensity of the transmitted light beamimmediately after passing through the polarizer, and theta is the angular differencebetween the polarization angle of the incident beam and thetransmission axis of the polarizer. After passing through thepolarizer, the transmitted light is polarized in the direction ofthe transmission axis of the polarizing filter. transmission axis. Hence it is possible for light to pass through apair of crossed polarizers if a third polarizer is inserted betweenthem with an intermediate transmission axis direction. What is thenew intensity I_2 of the light emerging from the finalpolarizer in Part E if a third polarizer (Polarizer A in the figure (PartF Figure) ), whose transmission axis is offset 45 degrees from each of theothers, is inserted between the original two polarizers? Express your answer as a decimalnumber times the symbol I_0. For example, if I_2 = (1/4)I_0, enter 0.25 *I_0 I_2 = ???
Explanation / Answer
The first polarizer does not change the intensity of thenatural incident light, only polarizes it in a certain direction.After the first polarizer, the intensity is still Io.The next polarizer increases the angle by 45o, soI1 = Iocos2(45) =Io(1/2). The next polarizer increases the angle by another45o, making it 90o. I2 =I1cos2(45) = (0.5 Io)(1/2) = (1/4)Io.
