A linearly polarized electromagnetic wave has an average intensity of 192 W/m 2
ID: 1902106 • Letter: A
Question
A linearly polarized electromagnetic wave has an average intensity of 192 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 = 37.7? with the incident electric field. Polarizer B has its axis at an angle of ?2 = 78.8? with the incident electric field, as shown in the figure.
What is the average intensity of the wave after it passes through polarizer A?
What is the average intensity of the wave after it passes through polarizer B?
Suppose that the two polarizers A and B are interchanged. What would the average intensity be after passing through both polarizers?
Explanation / Answer
given So=192W/m2 ,1=37.7o,2=78.80
a)After passing through polarizer A which has the polarizing axis an angle 1 from perpendicular, the intensity is
SA=Socos21 =192*cos237.7 =120.2W/m2
b)After the light passes through the second filter, its intensity drops again. However,its initial intensity is that of the light after it passes through filter A. Also,the angle between that which the light is traveling and that which it must passthrough is 2-1 .This is because the first polarizing filter only let light through
at that angle. Thus,
SB=SAcos2(2-1) =12cos2(78.8-37.7) =68.26 W/m2
c)If the filters are reversed, the intensity is not the same. The calculation is nearly the same, however. The intensity after passing through the first filter is now
SB=Socos22 =192*cos278.8=7.24W/m2
The angle between the pass axis of the two filters is the same regardless of their orientation. That is, it does not matter which way the light is oriented toward the other filter as it will be the same angle difference. Thus, the intensity after passing through the second filter is then
SA=SBcos2(2-1)=7.24cos2(78.8-37.7) =4.1 W/m2
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