A linearly polarized electromagnetic wave has an average intensity of 352 W/m 2

Question

A linearly polarized electromagnetic wave has an average intensity of 352 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 = 34.6° with the incident electric field. Polarizer B has its axis at an angle of 2 = 67.8° 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

Io =352 W/m^2, 1 = 34.6° 2 = 67.8°

From malus law

I = Iocos^2

After passing through IA = Io cos^21

After the light passes through the second filter, its intensity drops again. How-ever, 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 pass through is 2 1. This is because the first polarizing filter only let light through at that angle.

IB = IA cos^2(2 -1) = Iocos^21 *cos^2(2 -1)

IB = 352*cos^2(34.6)*cos^2(67.8 -34.6)

IB = 167 W/m^2

if first passing through B

IA = Iocos^22 *cos^2(2 -1)

IA = 352*cos^2(67.8)*cos^2(67.8 -34.6)

IA = 35.186 W/m^2

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