#Malus's law

Polarization and Malus Law

What is the intensity of light after passing through a polaroid rotated at \( 30^\circ \) relative to the initial polari

**Polarization** transverse wave property, light after polaroid polarized along pass-axis, Malus law I = I₀ cos²θ, θ angle between pass-axes, initial unpolarized intensity I₀ after first polaroid I₁ = I₀/2, after second at 45° I₂ = I₁ cos²45°= I₀/2×0.5= I₀/4, after two perpendicular 90° I=0 because cos90°=0, for 60° I= I₀/2×cos²60°= I₀/2×0.25= I₀/8. Using Malus’ law, I = I₀ cos² θ . For θ = 30° , cos 30° = (√(3)/2) , I = I₀ ((√(3)/2))² = I₀ × (3/4) = 0.75 I₀ . Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n =

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Polarization and Malus Law

What is the intensity of light after passing through two polaroids with pass-axes at \( 60^\circ \), if the intensity af

**Polaroid rotation** intensity varies sinusoidally with angle due to Malus law I = I₀ cos²θ, when polaroid rotated 90° from initial, intensity goes from max to zero, for unpolarized light rotating polaroid does not change intensity after first polaroid because average, but second polaroid intensity depends on relative angle, explains why intensity transmitted through two polaroids drops to zero when perpendicular. Using Malus’ law, I = I₀ cos² θ . For θ = 60° , cos 60° = 0.5 , I = I₀ (0.5)² = 0.25 I₀ . Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I =

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Wavefront and Huygens Principle

Why does the intensity of transmitted light through a polaroid decrease when rotated, even if the incident light is unpo

**Wavefront types** point source spherical, distant point source plane, after convex lens plane wave focuses to point because lens adds phase delay proportional to thickness, converging spherical wavefront, after concave mirror plane wave becomes spherical converging to focus, illustrating Huygens construction. Unpolarized light becomes polarized after the first polaroid, and the second polaroid’s pass-axis alignment determines the transmitted component, reducing intensity as the angle increases. Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC = 1/n, λ' = λ/n and A = 2

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Polarization and Malus Law

Why does the intensity of light transmitted through two polaroids drop to zero when their pass-axes are perpendicular?

**Polarization** transverse wave property, light after polaroid polarized along pass-axis, Malus law I = I₀ cos²θ, θ angle between pass-axes, initial unpolarized intensity I₀ after first polaroid I₁ = I₀/2, after second at 45° I₂ = I₁ cos²45°= I₀/2×0.5= I₀/4, after two perpendicular 90° I=0 because cos90°=0, for 60° I= I₀/2×cos²60°= I₀/2×0.25= I₀/8. When pass-axes are perpendicular, the electric field component along the second polaroid’s axis is zero (cos 90° = 0), blocking all light per Malus’ law. Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC = 1/n, λ' =

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Polarization and Malus Law

What is the intensity of light transmitted through two polaroids with their pass-axes at \( 45^\circ \) to each other, i

**Polaroid rotation** intensity varies sinusoidally with angle due to Malus law I = I₀ cos²θ, when polaroid rotated 90° from initial, intensity goes from max to zero, for unpolarized light rotating polaroid does not change intensity after first polaroid because average, but second polaroid intensity depends on relative angle, explains why intensity transmitted through two polaroids drops to zero when perpendicular. Using Malus’ law, I = I₀ cos² θ . For θ = 45° , cos 45° = (√(2)/2) , so I = I₀ ((√(2)/2))² = I₀ × (1/2) = (I₀/2) . Using Δ = d sinθ, y = n λ D/d, a sinθ =

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