Question

Three ideal polarizing filters are stacked, with the polarizing axis of the second and third filters at 21⁰ and 61⁰, respectively, to that of the first. If unpolarized light is incident on the stack, the light has intensity 60.0 w/cm² after it passes through the stack.

If the incident intensity is kept constant:

(a) What is the intensity of the light after it has passed through the stack if the second polarizer is removed?
(b) What is the intensity of the light after it has passed through the stack if the third polarizer is removed?

Answer 1

Apply Malus' law for light passing between two polarizing filters:

I = I₀cos²(θ)

I is the intensity after passing through, I₀ is the original intensity, and θ is the relative angle between the two filters.

For light passing through more than two filters, keep multiplying I₀ by cos²(θ) for each filter.

First let's solve for I₀ so we can answer parts a and b. We have three filters, so:

I = I₀cos²(θ₁)cos²(θ₂)

Given values:

I = 60.0W/cm²

θ₁ = 21°

θ₂ = 40° (we care about the relative angle between polarizers 2 & 3, not 1 & 3)

Plug in the values and solve for I₀:

60.0 = I₀cos²(21°)cos²(40°)

I₀ = 117W/cm²

a) Remove the second filter. Now the light passing through filter 1 only passes through filter 3. To find the resulting intensity:

I = I₀cos²(θ)

Where θ = 61° (relative angle between filter 1 & 3)

I = 117cos²(61°)

I = 27.5W/cm²

b) Remove the third filter. Now the light passing through filter 1 only passes through filter 2. To find the resulting intensity:

I = I₀cos²(θ)

Where θ = 21° (relative angle between filter 1 & 2)

I = 117cos²(21°)

I = 102W/cm²