Question

A horizontal beam of unpolarized light is incident on a stack of three polarizing filters with their polarization axes oriented, in sequence, 30◦, 60◦ and 90◦ clockwise from the vertical. The intensity of the light emerging from the stack is measured to be 275 W/m2. What is the intensity of the emerging light (in W/m2) if the middle polarizing filter is removed?

Answer 1

Answer:

122.22 W/m²

Explanation:

Let the intensity of unpolarized light is Io.

from first polariser

I' = Io/2

From second polariser

I'' = I' Cos²30 = 3 Io/8

From third polariser

I''' = I'' Cos²30 = 9Io/32

According to the question

9Io/32 = 275

Io = 977.78 watt/m²

Now, from first polariser

I' = Io/2 = 977.78 / 2 = 488.89 W/m²

I'' = 488.89 x cos²60 = 122.22 W/m²

thus, the intensity of light is 122.22 W/m².

Answer 2

Answer:

Explanation:

Given

Intensity of light emerging out is $I=275 W/m^2$

Polarizer axis are inclined at $30^{\circ}] , [tex]60^{\circ}$ , $90^{\circ}$

If $I_0$ is the Intensity of Incoming light then

$275=\frac{I_0}{2}\times \cos ^2{30}\times \cos^2 {30}$

as they are inclined to $30^{\circ}$to each other

$I_0=\frac{275}{9}\times 32$

$I_0=977.77 W/m^2$

If middle Filter is removed then

$I=0.5\cdot I_0\cos ^2{60}$

$I=0.5\cdot 977.77\cdot \frac{1}{4}$

$I=122.22 W/m^2$