Polarisation of light

What is polarisation?

In plain words: shake a rope up and down through a vertical fence and the wave gets through; shake it sideways and the fence stops it. A polaroid is a fence for the electric field of light. Careful: its molecules are not the fence’s bars. The field along the molecules is absorbed, so the pass axis is perpendicular to them. Ordinary light shakes in every direction, so a polaroid lets half of it through, and a second polaroid can then let through anything from all of that half to none, depending on how it is turned.

Ideal model: these intensity formulas assume perfect linear polarisers transmitting the pass-axis component without loss and completely blocking the orthogonal one; real sheets have absorption and finite leakage. E is transverse for the plane waves in vacuum or isotropic media considered here. Circular and elliptical light are also polarised: an electric-field direction that changes regularly is not unpolarised. A rotating linear analyser alone cannot distinguish circular from unpolarised light, since both give constant intensity.

Plane-polarised and unpolarised waves

• Move one end of a long horizontal string up and down: a wave travels along +x with displacement y(x, t) = a sin(kx − ωt), where k = 2π/λ (NCERT Eqs. (10.15)–(10.16), page 269, Figure 10.17). This is the travelling wave of Class 11.
• The displacement (along y) is at right angles to the direction of travel, so the wave is transverse. It is called y-polarised; since each point moves on a straight line it is linearly polarised, and since the string stays in the x-y plane it is plane polarised (NCERT pages 269–270).
• Shaking the string in the x-z plane gives a z-polarised wave, z(x, t) = a sin(kx − ωt) (NCERT Eq. (10.17), page 270).
• If the plane of vibration changes randomly in very short intervals, the wave is unpolarised: the displacement changes direction randomly but is always perpendicular to the direction of travel (NCERT page 270).
• Natural light from an ordinary thermal source is often modelled as unpolarised before reflection or scattering: its electric vector takes all possible directions in the transverse plane, rapidly and randomly (NCERT Summary, page 272).
• Only transverse waves can be polarised. Most interference and diffraction effects exist for longitudinal waves such as sound in air too, but polarisation is special to transverse waves like light (NCERT Points to ponder, page 272). See transverse and longitudinal waves.

Polaroids and the pass axis

• A polaroid is a thin plastic-like sheet of long-chain molecules aligned in one direction. The electric field along the molecules is absorbed. Unpolarised light that passes through comes out linearly polarised, with its electric field perpendicular to the molecules; that direction is the pass axis (NCERT page 270).
• One polaroid: light from an ordinary source, such as a sodium lamp, comes out of a polaroid P₁ with half its intensity, and turning P₁ changes nothing (NCERT page 270). The half is the average of cos² θ over all the random directions of the incoming field (reasoned).

• Two polaroids: put a second, identical polaroid P₂ before P₁, so the light now meets P₂ first. Now turning P₁ has a dramatic effect: in one position almost no light gets through both, and turned 90° from there, P₁ passes nearly all the light coming from P₂ (NCERT page 270, Figure 10.18).

Malus’ law

• Light leaving the first polaroid is polarised along that polaroid’s pass axis. If the pass axes of the two polaroids make an angle θ, only the component E cos θ along the second pass axis gets through. The intensity goes as the square of the field, so (NCERT Eq. (10.18), page 270):

• Here I₀ is the intensity of the polarised light after the first polaroid. The second polaroid can therefore control the light from 50% of the original unpolarised intensity down to zero (NCERT page 271).
• Turning the second polaroid through a full circle, 2π, gives two maxima (θ = 0 and π) and two minima (θ = π/2 and 3π/2) (NCERT Summary, page 272).
• NCERT slip (page 270): NCERT places P₂ before P₁ and says the light is polarised by P₂, but then writes that “the component E cos θ (along the pass-axis of P₂) will pass through P₂”, and that I₀ is the intensity “after passing through P₁”. With P₂ first, the component along the pass axis of P₁ passes through P₁, and I₀ is the intensity after P₂. The law itself is unaffected.

Uses of polaroids

• Polaroids are used to control intensity, in sunglasses and windowpanes, and in photographic cameras and 3D movie cameras (NCERT page 271).
• Three polaroids: a polaroid turned between two crossed polaroids lets light through, most of all when it is at 45° to both (NCERT Example 10.2, page 271; see Example 2 below).
• Polaroid sunglasses also cut glare: light reflected from water or a road is partly polarised, horizontally, so a vertical pass axis blocks much of it (beyond the NCERT text).

Solved examples

Common mistakes to avoid

Quick revision summary

• Light is transverse, so it can be polarised; sound in air cannot.
• Plane (linearly) polarised: the field vibrates in one direction; unpolarised: the direction changes rapidly and randomly.
• A polaroid passes the field along its pass axis; unpolarised light through one polaroid: I = I_u/2.
• Malus’ law: I = I₀ cos² θ, with θ the angle between the pass axes; two maxima and two minima per turn.
• A polaroid between crossed polaroids passes (I₀/4) sin² 2θ, at most I₀/4 at 45°.
• Uses: controlling intensity, sunglasses, windowpanes, cameras, 3D films.

Questions students ask

How are polarised sunglasses different from ordinary tinted sunglasses?

Polarised sunglasses, which NCERT lists as a use of polaroids (page 271), dim all light like tinted lenses but, beyond the NCERT text, also have a vertical pass axis that blocks much of the glare from water and wet roads, which is partly polarised with its field horizontal. To test a pair, look through one lens at a display known to emit linearly polarised light, such as a suitable LCD, and turn the glasses slowly through half a turn: a linear polarising lens gives a strong brightness variation while a simple isotropic tint does not. Some displays emit circular or otherwise modified polarisation, so a negative screen test is inconclusive. That effect on cockpit displays is one reason the US FAA advises pilots against polarised lenses (brochure “Sunglasses for Pilots”).

What are the types of polarisation of light?

Polarised light is of three types: linear (plane), with the electric field vibrating along one fixed line; circular, with the field’s direction turning round once every period at constant size; and elliptical, with its tip tracing an ellipse (beyond the NCERT text and both syllabuses, which treat only plane polarisation). Two coherent equal-amplitude components at right angles, a quarter of a cycle (90°) out of phase, give circular light; most other combinations give elliptical light. A circular-polarisation stereoscopic system can encode the two eye images with opposite handedness; unlike linear axes, handedness does not change when the viewer rolls their head (reasoned beyond NCERT; page 271 names polaroids in 3D movie cameras).

How can plane-polarised light be produced?

Plane-polarised light can be produced in four main ways: by a polaroid, which absorbs the field along its aligned molecules (NCERT page 270); and, beyond the NCERT text, by reflection at the Brewster angle, by scattering, since sunlight scattered at right angles by air molecules is strongly polarised, and by double refraction in calcite, whose two beams are polarised at right angles (beyond NCERT: Huygens’ Treatise on Light and modern transverse-wave interpretation), as in the Nicol prism of NCERT Class 12 Chemistry Part II (page 175). Scattering and reflection were Sections 10.7.1 and 10.7.2 of NCERT’s 2021–22 reprint, dropped in 2022 (NCERT rationalised-content list, Class XII, page 51).

Why is plane-polarised light used to study optical isomers?

Plane-polarised light is used to study optical isomers because a pure enantiomer pair has the same ordinary physical properties in an achiral environment but rotates plane-polarised light by equal and opposite angles under matching wavelength, temperature, solvent, path length and concentration. They can behave differently in chiral chemical or biological environments; optical rotation is not their only possible difference. The sign convention is clockwise for the dextrorotatory (+) form, anticlockwise for the laevorotatory (−) form (NCERT Class 12 Chemistry Part II, pages 175 and 177). A polarimeter measures the angle: light from a Nicol prism crosses the solution, and an analyser is turned to find the new plane. A 50:50 racemic mixture gives no rotation, as the two cancel (stereoisomerism).

Is Malus’ law in the JEE Main and NEET syllabus?

Malus’ law is not named in either syllabus, but it is the working law of the polarisation topics both list: Unit 16 of the JEE Main syllabus lists “plane-polarized light, Brewster’s law, uses of plane-polarized light and Polaroid”, NEET (UG) 2026 Unit 16 has the same topics, and NCERT Class 12 Physics Part II gives Malus’ law as Eq. (10.18) in Section 10.7 (page 270). Any question on how much light gets through two or more polaroids rests on it, as in NCERT Example 10.2 (page 271). Brewster’s law, also listed, has no section in the 2026–27 book.

Who discovered the polarisation of light?

The polarisation of light was named by the French physicist Étienne-Louis Malus, who found it in reflected light: looking through a doubly refracting crystal at sunlight reflected from the windows of the Luxembourg Palace in Paris, he saw that it was polarised, and reported the discovery in 1808 (beyond NCERT: François Arago, Malus, chapter VIII, including the memoir of 12 December 1808). NCERT’s Malus’ law, Eq. (10.18) on page 270, bears his name. Huygens had described, but not explained, the effect in calcite in his Treatise of 1690, and in 1815 David Brewster, crediting Malus, found the law for the angle of complete polarisation (Philosophical Transactions, volume 105).

Practice questions

Try each question first, then open the answer to check your working.

1. Q1. Polarised light of intensity 10 W/m² meets a polaroid whose pass axis is at 45° to the light’s field. What comes through?

   Show answerHide answer

   10 × cos² 45° = 10 × 1/2 = 5.0 W/m² (NCERT Eq. (10.18), page 270).

2. Q2. Two polaroids are crossed. What fraction of unpolarised light gets through?

   Show answerHide answer

   None: after the first, the light is polarised along its axis, and the second, at 90°, passes cos² 90° = 0 of it (NCERT pages 270–271).

3. Q3. Why does polarisation show that light waves are transverse?

   Show answerHide answer

   Only a transverse wave has a direction of vibration across its path that a polaroid can select; a longitudinal wave such as sound in air cannot be polarised (NCERT pages 270 and 272).