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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 :

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

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