A linearly polarized electromagnetic wave has an average intensity of 115 W/m2.

Question

A linearly polarized electromagnetic wave has an average intensity of 115 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 = 22.4° with the incident electric field. Polarizer B has its axis at an angle of ?2 = 76.9° 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

here,

initial intensity of the polarized light , I0 = 115 W/m^2

theta1 = 22.4 degree

theta2 = 76.9 degree

the average intensity of the wave after it passes through polarizer A , I1 = I0*(cos(theta1))^2

I1 = 115 * (cos(22.4))^2

I1 = 98.3 W / m^2

the average intensity of the wave after it passes through polarizer A is 98.3 W/m^2

the average intensity of the wave after it passes through polarizer B , I2 = I1 * (cos(theta1 - theta2))^2

I2 = 98.3 * ( cos( theta2 - theta1))^2

I2 = 98.3 * (cos(54.5 ))^2

I2 = 33.15 W/m^2

if the polarizers are interchanged

the average intensity of the wave after it passes through polarizer A , I1' = I0*(cos( theta2))^2

I1' = 115 * (cos(76.9))^2

I1' = 5.91 W / m^2

the average intensity of the wave after it passes through polarizer A is 5.91 W/m^2

the average intensity of the wave after it passes through polarizer B , I2' = I1' * (cos(theta2 - theta1))^2

I2' = 5.91 * ( cos( theta2 - theta1))^2

I2' = 5.91 * (cos(54.5 ))^2

I2' = 1.99 W/m^2

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