A linearly polarized electromagnetic wave has an average intensity of 358 W/m 2

Question

A linearly polarized electromagnetic wave has an average intensity of 358 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 = 38.9

A linearly polarized electromagnetic wave has an average intensity of 358 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 = 38.9° with the incident electric field. Polarizer B has its axis at an angle of ?2 = 63.4° with the incident electric field, as shown in the figure. a) What is the average intensity of the wave after it passes through polarizer A? b) What is the average intensity of the wave after it passes through polarizer B? c) Suppose that the two polarizers A and B are interchanged. What would the average intensity be after passing through both polarizers?

Explanation / Answer

A) LInearly polarized electromagnetoic wave has an average intensity
Io = 358 W/m^2

@1 = 38.9

@ = 63.4

According to Malus Law ,

After passing through polarizer A, the transmitted intensity ,

Ia = Io cos^2(@1)

      = 358 cos^2(38.9) = 216.83 W/m^2

B) After light passes through teh second filter, its intensity drops again.
However, its initial intensity is that of the light after passing through filter A
Also the angle between that which the light travelling and that which it must pass through an angle = (@2 - @1)

Ib = Ia cos^2 (@2 -@1)

    = 216.83 cos^2 (63.4 - 38.9) =179.54 W/m^2

C) If filters are interchanged,
The intensity of light after passing through first filter is,
Ib = Io cos^2(63.4)
= 358 cos^2(63.4) = 71.77 W/m^2

and

Ia = Ib cos^2(63.4 - 38.9) = 59.43 W/m^2
                           

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