Physic Labs

Optics

Polarization of light

Rotate an analyzer relative to a polarizer and verify Malus's law I=I0cos⁡2θI=I_0\cos^2\theta for linearly polarized light, by reading the transmitted intensity and the electric-field projection at several angles.

Undergraduate

⚠ Polarization demos often use lasers or bright LEDs; never look into the beam, even through a polarizer.

Equipment

  • Virtual polarizer–analyzer pair with field-vector display
  • Slider “Góc phân tích θ” (analyzer angle)
  • Slider “Cường độ ban đầu I₀” (initial intensity)
  • “Đặt lại tham số” (reset) button; transmitted-intensity readout

Procedure

  1. Scan the analyzer angle

    Drag the θ slider slowly from 0° to 180° and read the transmitted intensity. It is maximal at θ=0°, falls to zero at θ=90° (crossed polarizers) and recovers at 180° — the cos⁡2θ\cos^2\theta signature of projecting the field onto the analyzer axis.

  2. Test cos²θ quantitatively

    Set θ to 30°, 45° and 60° and record I at each. Compare the ratios I/I0I/I_0 with cos⁡2θ\cos^2\theta: expect 0.75, 0.50 and 0.25. The electric field is transmitted as Ecos⁡θE\cos\theta, so intensity, proportional to E2E^2, follows cos⁡2θ\cos^2\theta.

  3. Scale the initial intensity

    Move the I₀ slider and confirm the cos² shape is preserved — only the scale changes. Then predict the reading for θ=0° and θ=90° at a new I₀ before measuring, and explain why a real polarizer also absorbs about half of unpolarized incident light.

Simulation

Experiment history

Étienne-Louis Malus discovered in 1808 that light reflected from a window is polarized — the name comes from the “poles” of Newton's particle picture — and found empirically that an analyzer transmits intensity proportional to cos⁡2θ\cos^2\theta. Augustin Fresnel soon reinterpreted the effect with transverse waves in the 1820s. The electromagnetic foundation arrived with Maxwell's equations (1865), which made polarization a property of the transverse E field. Polaroid sheet polarizers, invented by Edwin Land in 1928, turned the effect into everyday technology — camera filters, sunglasses, and the liquid-crystal displays that depend on voltage-controlled polarization.

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