Question

Unpolarized light of intensity 800 W/m2 is incident on two ideal polarizing sheets that are placed with their transmission axes perpendicular to each other. An additional polarizing sheet is then placed between the two, with its transmission axis oriented at 30∘ to that of the first. What is the intensity of the light passing through the stack of polarizing sheets? (Express your answer to two significant figures.)

Answer 1

Answer:

75 W/m²

Explanation:

$I_0$ = Unpolarized light intensity = 800 W/m²

$\theta$ = Angle between filters = 30°

Intensity of light after passing through first polarizer

$I=\frac{I_0}{2}\\\Rightarrow I=\frac{800}{2}\\\Rightarrow I=400\ W/m^2$

Intensity of light after passing through second polarizer

$I_1=Icos^2\theta\\\Rightarrow I_1=400\times cos^2(30)\\\Rightarrow I_1=300\ W/m^2$

Intensity of light after passing through third polarizer

$I_2=I_1cos^2\theta\\\Rightarrow I_2=300\times cos^2(90-30)\\\Rightarrow I_1=75\ W/m^2$

The intensity of the light passing through the stack of polarizing sheets is 75 W/m²