Polaroids and Malus' law.

• Place a second identical polaroid in the beam. Now rotating one of them has a striking effect: at one setting almost no light gets through the pair, and 90° from that setting nearly all the light leaving the first polaroid passes the second.
• Why: the light leaving the first polaroid has its electric field along that polaroid's pass-axis. If the second pass-axis makes an angle θ with the first, only the component E cos θ along it gets through.
• Intensity goes as the square of the field, so I = I₀ cos²θ. This is Malus' law, where I₀ is the intensity of the polarised light that left the first polaroid.
• θ = 0 passes all of I₀; θ = 90° (crossed polaroids) passes nothing; θ = 45° passes I₀/2. In one full turn of the second polaroid, through 2π, the intensity goes through two maxima and two minima.
• One polaroid halves unpolarised light, so a pair can set the transmitted light anywhere from 50% of the original intensity down to zero just by changing the angle between their axes.
• Example 10.2: a polaroid P₂ is rotated between two crossed polaroids P₁ and P₃. After P₂ the intensity is I₀cos²θ. The angle between P₂ and P₃ is π/2 − θ, so the light leaving P₃ is I₀cos²θ sin²θ = (I₀/4) sin²2θ.
• That is zero when P₂ lines up with either crossed polaroid (θ = 0 or π/2) and greatest, I₀/4, when θ = π/4. Inserting a third sheet lets light through a pair that on its own would block it completely.
• Polaroids control intensity in sunglasses and window panes, and are used in photographic cameras and 3D movie cameras.

Teaching this idea? Put the simulation on your own page or LMS with this code.