Question

Originally, light is unpolarized. It then travels through 3 polarizers: the first with its transmission axis aligned vertical, the next at a 30 degree angle to the vertical and the last aligned at a 45 degree angle to the vertical (tilted the same direction as the first with respect to the vertical). The original intensity of light is 4 W/m2.

1-What is the intensity of light after the second polarizer?

2-What is the intensity of light after the third polarizer?

3-If the second polarizer is aligned at a 45 degree angle to the vertical (just like the third), what is the final intensity of light after the third polarizer?

4- If the second polarizer is aligned at a 45 degree angle to the vertical (but in the other direction), what is the final intensity of light after the third polarizer?

Answer 1

Given,

Given, I₀ = 44 W/m²

First polariser is aligned vertically,

After passing through first polariser, I₁ = 0.5*I₀

Now,

Angle between first polariser and second polariser is 30 degrees

We know,

Intensity after passing through second polariser is

=> I₂ = I₁*cos² = (0.5*I₀)*cos²(30)

          = (0.5*I₀)*0.75 = 0.375*I₀

          = 0.375*4 = 1.5 W/m²

(2)

Now,

Angle between second polariser and third polariser is (45-30) = 15 degrees

We know,

Intensity after passing through Third polariser is

=> I₃ = I₂*cos² = (0.375*I₀)*cos²(15)

          = (0.375*I₀)*0.933 = 0.35*I₀

          = 0.35*4 = 1.4 W/m²

(3)

If second polariser is at 45 degrees

then angle between second and third polariser is zero.

So,

Intensity after passing through Third polariser is

=> I₃ = I₂*cos² = (0.375*I₀)*cos²(0)

          = 0.375*I₀ = 0.375*4

          = 1.5 W/m²

(4)

If second polariser is at 45 degrees on the other side

then angle between second and third polariser is 90 degrees.

So,

Intensity after passing through Third polariser is

=> I₃ = I₂*cos² = (0.375*I₀)*cos²(90)

          = 0.375*I₀*0

          = 0