Polarization

SYLLABUS

Phenomenon of polarization, Brewster’s law; transverse nature of light, Polaroid.

What is This Chapter About?

Hold a piece of polarising film up to the sky on a clear day. Now rotate it slowly. You will notice the sky appears to brighten and darken as you rotate the film. Place two pieces of polarising film on top of each other and rotate one relative to the other — at one angle they are almost transparent, at another they block virtually all light. These striking observations reveal something profound about the nature of light: it is a transverse wave, and its oscillations have a definite direction.

Polarization is the phenomenon that distinguishes transverse waves from longitudinal ones. Sound waves — longitudinal — cannot be polarized. Light waves — transverse electromagnetic oscillations — can be. The ability to polarize light is therefore direct experimental proof of its transverse wave nature, and it has given rise to enormously important technologies from LCD screens and camera filters to 3D cinema and stress analysis in engineering.

Chapter 13 of NEB Grade 12 Physics carries 3 teaching hours and completes the wave optics section of the course, bringing together the wave theory of light that began in Chapter 10 and developed through interference (Chapter 11) and diffraction (Chapter 12).

Key Concepts You Will Learn

Transverse Nature of Light and Polarization

In an ordinary (unpolarized) light beam, the electric field oscillates in all directions perpendicular to the direction of propagation — up-down, left-right, and all angles in between — with equal probability. This is because ordinary light sources produce billions of photons, each with random oscillation directions.

Polarized light is light in which the electric field oscillates in only one specific direction perpendicular to propagation. This direction is called the plane of polarization (or plane of vibration).

The fact that light can be polarized — that it has a definite transverse oscillation direction that can be selected — proves conclusively that light is a transverse wave. Longitudinal waves (like sound) have no transverse oscillation direction to select, so they cannot be polarized. This is why the discovery of polarization in the early 19th century was decisive evidence for the wave theory of light.

Polaroids

A Polaroid is a sheet of material that transmits light vibrating in only one specific direction (the transmission axis) and absorbs light vibrating perpendicular to it. When unpolarized light passes through a Polaroid, the transmitted light is linearly polarized — its electric field oscillates only along the transmission axis. The Polaroid acts as a polarizer.

When polarized light passes through a second Polaroid (acting as an analyser) oriented at angle [latex]\theta[/latex] to the first, the transmitted intensity follows Malus’s Law:

[latex]I = I_0\cos^2\theta[/latex]

where [latex]I_0[/latex] is the intensity of the polarized light incident on the analyser. When [latex]\theta = 0°[/latex] (parallel transmission axes), all light passes through. When [latex]\theta = 90°[/latex] (crossed Polaroids), no light passes through — the output is completely dark. At intermediate angles, partial transmission occurs as given by Malus’s Law.

Malus’s Law is one of the most elegant and precisely verified results in optics. It confirms both the transverse nature of light and the vector nature of the electric field oscillation.

Brewster’s Law

When unpolarized light strikes a surface at a specific angle called the Brewster angle ([latex]\theta_B[/latex]), the reflected light is completely polarized — its electric field oscillates only parallel to the surface (perpendicular to the plane of incidence). The transmitted (refracted) light is partially polarized.

Brewster’s Law states that the Brewster angle satisfies:

[latex]\tan\theta_B = \frac{n_2}{n_1} = n[/latex]

where n is the refractive index of the second medium relative to the first. At the Brewster angle, the reflected and refracted rays are perpendicular to each other ([latex]\theta_B + \theta_r = 90°[/latex]).

Brewster’s Law has a beautiful physical explanation: when the refracted ray travels at 90° to where the reflected ray would be, the oscillating dipoles in the medium cannot radiate in the direction of the reflected ray for one polarization component — so only the other component is reflected.

Brewster’s Law is practically important for reducing glare. Polarizing sunglasses are oriented to block the horizontally polarized light reflected from horizontal surfaces like water and roads — the reflected glare is predominantly polarized at Brewster’s angle, so a vertically oriented Polaroid lens blocks most of it while transmitting the non-glare light.

Applications of Polarization

Polarization has a remarkably wide range of applications in modern technology and science.

LCD screens (liquid crystal displays) use polarization extensively. Two Polaroids are placed with their axes perpendicular (crossed), normally blocking all light. A liquid crystal layer between them can rotate the polarization of light passing through it when a voltage is applied, allowing light to pass through the second Polaroid and creating bright pixels. Without voltage, the liquid crystal does not rotate the polarization and the pixel remains dark.

3D cinema uses polarization to deliver different images to each eye. Two projectors show slightly different images polarized at different angles. The viewer wears glasses with correspondingly polarized lenses, so each eye sees only one image — creating the illusion of three-dimensional depth.

Stress analysis in engineering uses photoelasticity — transparent models of structures placed between crossed Polaroids reveal coloured fringe patterns when stressed, showing where stress concentrations are highest.

Photography uses polarizing filters to reduce reflections from glass and water, and to deepen the blue colour of the sky.

Polarimetry — measuring the rotation of polarized light by optically active substances like sugar solutions — is used in the food and pharmaceutical industries to determine concentration and purity.

Why This Chapter Matters for NEB Exams

Polarization is examined consistently in NEB Grade 12 Physics. The phenomenon of polarization as proof of the transverse nature of light is a standard conceptual question. Malus’s Law — stating it and applying it in numerical problems — appears regularly. Brewster’s Law — deriving [latex]\tan\theta_B = n[/latex] and calculating the Brewster angle for given refractive indices — is a classic examination question. Applications of polarization (LCD screens, polaroid sunglasses, 3D cinema) are popular questions connecting physics to everyday technology.

Important Topics to Focus On

• Distinction between unpolarized and polarized light
• Why polarization proves light is a transverse wave
• Why sound cannot be polarized (longitudinal wave)
• Polaroids as polarizers and analysers
• Malus’s Law: [latex]I = I_0\cos^2\theta[/latex] — derivation concept and numerical applications
• What happens at [latex]\theta = 0°[/latex], [latex]\theta = 45°[/latex], and [latex]\theta = 90°[/latex] between polarizer and analyser
• Brewster’s Law: [latex]\tan\theta_B = n[/latex] — statement and derivation concept
• Geometric proof that reflected and refracted rays are perpendicular at Brewster angle
• Polarizing sunglasses — why they reduce glare from horizontal surfaces
• Applications: LCD screens, 3D cinema, photography, photoelasticity, polarimetry
• Numerical problems on Malus’s Law and Brewster’s Law

Connection to Other Chapters

Polarization completes the wave optics sequence that began with Chapter 10 (Nature and Propagation of Light). Huygens’ wave theory established that light is a wave; interference (Chapter 11) showed superposition of light waves; diffraction (Chapter 12) showed bending of light waves; and polarization (Chapter 13) now reveals the transverse oscillation direction of those waves. Together these four chapters form the complete classical wave description of light. Polarization connects forward to Chapter 21 (Photons) — where the quantum nature of light is explored — and to Chapter 19 (Alternating Currents), where electromagnetic wave polarization has analogies in AC circuit theory. Brewster’s Law connects back to Chapter 15 of Grade 11 (Refraction at Plane Surfaces) through Snell’s Law and refractive index.