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

Step-by-step 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=(I_0)/(2)* \cos ^2{30}* \cos^2 {30}`

as they are inclined to
`30^(\circ)`to each other

`I_0=(275)/(9)* 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 (1)/(4)`

`I=122.22 W/m^2`

Answer 2

122.22 W/m²

Step-by-step 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.