Unpolarized light of intensity I₀ is made to pass through three polarizers P₁, P₂ and P₃ successively. The polarization axis of P₂ makes an angle of θ₁ with that of P₁, while that of P₃ makes an angle θ₂ with that of the P₂. What will be the intensity of light coming out of P₃?

Question

Accepted Answer

> [!TLDR]
> I₁ = I₀/2; I₂ = I₁cos²θ₁ = (I₀cos²θ₁)/2; I₃ = I₂cos²θ₂ = (I₀cos²θ₁cos²θ₂)/2.

The first polarizer P₁ plane-polarizes the unpolarized light and halves its intensity:

$$I_1 = \frac{I_0}{2}$$

Through P₂ (axis at θ₁ to P₁), by Malus' law:

$$I_2 = I_1\cos^2	heta_1 = \frac{I_0\cos^2	heta_1}{2}$$ …

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