4. Three polarizing disks whose planes are parallel and centered on common axis. The directions of their transmission axes relative to the vertical are respectively: θ1 = 40o clockwise, θ2 = 24o counter-clockwise, and θ3 = 26o clockwise. A beam of light polarized along the vertical is incident onto the first polarizer with an intensity of I0 = 28.0 W/m². Calculate the transmitted intensity through all three polarizers.

Answer

given,

θ₁ = 40⁰ clockwise,

θ₂ = 24⁰ counter-clockwise

θ₃ = 26⁰ clockwise

I₀ = 28.0 W/m²

the transmitted intensity through all three polarizers.

I₁ = I₀ (cos θ₁) ²

I₁ = 28 x (cos 40⁰) ²

I₁ = 16.43 W/m²

Intensity through second polarizer,

I₂ = I₀ (cos (θ₂ - θ₁)) ²

I₂ = 28 x (cos (-24-40)) ²

I₂ = 28 x (cos (-64)) ²

I₂ = 5.38 W/m²

Intensity through third polarizer,

I₃ = I₀ (cos (θ₃ - θ₂)) ²

I₃ = 28 x (cos (26 - (-24))) ²

I₃ = 28 x (cos (50)) ²

I₃ = 11.57 W/m²