A linearly polarized electromagnetic wave has an average intensity of 288 W/m 2
ID: 1290071 • Letter: A
Question
A linearly polarized electromagnetic wave has an average intensity of 288 W/m2. This wave is directed towards two ideal polarizers (in real polarizers, transmission is also effected by reflection and absorption). Polarizer A is oriented with its transmission axis at an angle of ?1 = 34.2 with the incident electric field. Polarizer B has its axis at an angle of ?2 = 63.0 with the incident electric field, as shown in the figure.
1. What is the average intensity of the wave after it passes through polarizer A?
2. What is the average intensity of the wave after it passes through polarizer B?
3. Suppose that the two polarizers A and B are interchanged. What would the average intensity be after passing through both polarizers?
A linearly polarized electromagnetic wave has an average intensity of 288 W/m2. This wave is directed towards two ideal polarizers (in real polarizers, transmission is also effected by reflection and absorption). Polarizer A is oriented with its transmission axis at an angle of ?1 = 34.2½ with the incident electric field. Polarizer B has its axis at an angle of ?2 = 63.0½ with the incident electric field, as shown in the figure. 1. What is the average intensity of the wave after it passes through polarizer A? 2. What is the average intensity of the wave after it passes through polarizer B? 3. Suppose that the two polarizers A and B are interchanged. What would the average intensity be after passing through both polarizers?Explanation / Answer
The Law of Malus states that the transmitted intensity is given by
S = S0 cos2(t).................here t represents theta
(a)
after passing through polarizer A which has the polarising axis an angle t1 from the perpendicular, the intensity is
SA = So cos2t1
SA = 288 * cos2(34.2)
SA = 197 W/m2
(b)
After the light passes through the second ?lter, its intensity drops again. However, its initial intensity is that of the light after it passes through ?lter A. Also, the angle between that which the light is traveling and that which it must pass through is t2 ? t1. This is because the ?rst polarizing ?lter only let light through at that angle. Thus,
SB = SA cos2(t2 - t1) = So cos2t1 cos2(t2 - t1)
SB = 197 * cos2(63 - 34.2)
SB = 151.28 W/m2
(c)
If the ?lters are reversed, the intensity is not the same. The calculation is nearly the same, however. The intensity after passing through the ?rst ?lter is now
SB = Socos2t2
SB = 288 * cos2(63)
SB = 59.36 W/m2
The angle between the pass axis of the two ?lters is the same regardless of their orientation. That is, it does not matter which way the light is oriented toward the other ?lter as it will be the same angle di?erence. Thus, the intensity after passing through the second ?lter is then
SA = SB cos2(t2 - t1)
SA = 59.36 * cos2(63 - 34.2)
SA = 45.58 W/m2
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