Polarisation
Section: Waves | Syllabus: Cambridge AS Level Physics 9702
Polarisation Polarisation is a phenomenon unique to transverse waves that restricts oscillations to a single plane. Key Definitions Polarisation : The process of restricting the oscillations of a transverse wave to a single plane.
Only transverse waves can be polarised. Unpolarised wave : A transverse wave in which oscillations occur in all planes perpendicular to the direction of wave travel. Plane-polarised wave : A transverse wave in which oscillations occur in only one plane (which contains the direction of wave travel).
Polarising filter (polariser) : A device that transmits oscillations in only one plane while absorbing oscillations in perpendicular planes. Transmission axis : The plane of oscillation that a polariser allows through.
Core Principles Why Only Transverse Waves Can Be Polarised In transverse waves, oscillations are perpendicular to the direction of travel These perpendicular oscillations can occur in any plane A polariser can select just one of these planes In longitudinal waves, oscillations are parallel to wave travel-there is only one possible direction, so polarisation is not applicable Unpolarised Light Light from most sources (sun, bulbs) is unpolarised Contains oscillations in all planes perpendicular to the direction of travel Can be represented as oscillations in all directions in a plane perpendicular to the ray Effect of a Single Polariser on Unpolarised Light The transmitted light is plane-polarised The intensity is reduced to half: I = I₀/2 (This halving is not required for calculations at AS Level) Effect of a Polariser on Plane-Polarised Light The transmitted intensity depends on the angle between the polarisation plane and the transmission axis This is described by Malus's law FIG 7.7: Polarisation of Light Show the concept of polarisation: (a) Unpolarised light represented as arrows oscillating in all planes perpendicular to the direction of travel.
(b) Light passing through a polariser showing only vertical oscillations transmitted. (c) Two polarisers: when aligned (parallel), light passes through; when crossed (90°), no light passes. Label the transmission axis of each polariser.
Malus's Law When plane-polarised light of intensity I₀ passes through a polarising filter (analyser), the transmitted intensity is: I = I_0 ^2θ where: I = transmitted intensity (W m⁻²) I₀ = incident intensity of plane-polarised light (W m⁻²) θ = angle between the plane of polarisation and the transmission axis of the filter Key Cases Angle θ Transmitted Intensity Result 0° I = I₀ cos²(0°) = I₀ × 1 I₀ (maximum transmission) 90° I = I₀ cos²(90°) = I₀ × 0 0 (no transmission-crossed polarisers) 45° I = I₀ cos²(45°) = I₀ × 0.5 0.5I₀ (half transmitted) 60° I = I₀ cos²(60°) = I₀ × 0.25 0.25I₀ (quarter transmitted) Concept Insight: Rope and Fence Analogy Imagine sending waves along a rope that passes through a vertical fence slot: Vertical oscillations pass through unaffected Horizontal oscillations are blocked completely Oscillations at an angle have only their vertical component transmitted The fence slot acts like a polarising filter: Its orientation determines which oscillation plane is transmitted Only the component of oscillation parallel to the slot passes through With two fence slots: If both are vertical (parallel): waves pass through both If one is vertical and one horizontal (perpendicular/crossed): waves are blocked If at some angle between: partial transmission occurs Series of Polarisers When light passes through multiple polarisers in series, apply Malus's law at each stage: Two polarisers at angle θ to each other: I_final = I_0 ^2θ Three polarisers (first and third crossed at 90°, middle at angle θ to first): After first polariser: light is plane-polarised with intensity I₁ After second polariser (at angle θ): I₂ = I₁ cos²θ After third polariser (at angle (90° − θ) to second): I₃ = I₂ cos²(90° − θ) = I₂ sin²θ Combined: I₃ = I₁ cos²θ sin²θ Key Point With three polarisers, light CAN pass through crossed polarisers if an intermediate polariser is inserted at an angle.
Worked Examples Worked Example 1: Single Polariser Question: Plane-polarised light of intensity 20 W m⁻² passes through a polariser with its transmission axis at 30° to the plane of polarisation. Calculate the transmitted intensity.
Solution Using Malus's law: I = I_0 ^2θ = 20 × ^2(30°) I = 20 × (0.866)^2 = 20 × 0.75 = 15 W m^-2 Worked Example 2: Crossed Polarisers Question: Two polarising filters are placed with their transmission axes perpendicular to each other (crossed).
Plane-polarised light of intensity 50 W m⁻² (with polarisation parallel to the first filter) is incident on the first filter. Calculate the intensity after: (a) the first filter, (b) the second filter.
Solution (a) The incident light is already polarised parallel to the first filter (θ = 0°): I_1 = I_0 ^2(0°) = 50 × 1 = 50 W m^-2 (b) The second filter is at 90° to the first, so θ = 90°: I_2 = I_1 ^2(90°) = 50 × 0 = 0 W m^-2 No light passes through cro…
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