Because light is a transverse wave, polarization exists, in which the direction of vibration is aligned in a particular direction. We will understand applications ranging from polarizing plates and Brewster’s angle to liquid-crystal displays.
Basic Knowledge
Ordinary light (unpolarized light) is a collection of transverse waves whose directions of vibration are random (unpolarized light).
Polarized light: Light whose electric-field vibration is aligned in one direction.
Polarizing plate (polarizing filter): Allows only the vibration component in a particular direction to pass. When two polarizing plates are placed perpendicular to each other (90°), no light passes through (extinction).
Malus’s law: For incident polarized intensity I₀, when the polarizing plate is tilted by angle φ, the transmitted intensity is:
I = I₀ cos² φ
Brewster’s angle θB: The angle at which the reflected component of incident light becomes completely polarized.
tan θB = n₂/n₁
（At this angle, the reflected and refracted rays are at 90° to each other）
Polarization（Light whose electric-field vibration direction is aligned in one direction）
Polarizer（An optical element that transmits only the vibration component in one direction）
Malus’s law（I = I₀ cos² φ. The relationship between the angle of polarizers and transmitted intensity）
Brewster’s angle θB（tan θB = n₂/n₁. The angle of incidence at which reflected light becomes completely polarized）
Liquid crystal（A material whose polarization direction of light can be controlled by an electric field. The principle of LCDs）
Further Study (Background・Significance)
The fact that light is a transverse wave is decisively demonstrated by polarization. A longitudinal wave does not undergo extinction by a polarizing plate. This contrasts with sound waves (longitudinal waves), for which “polarization” cannot be defined.
A liquid-crystal display (LCD) combines two polarizing plates with liquid-crystal molecules whose orientation changes in an electric field. By changing the orientation of the liquid crystals with voltage, the transmission and blocking of light are controlled. Smartphones and PC monitors all use this principle.
Many sunglasses contain polarizers that block reflected light from water surfaces and roads (which is mainly polarized near Brewster’s angle), reducing glare.
- Polarization is evidence that light is a transverse wave
- Two polarizing plates at 90° cause extinction (zero light)
- Malus’s law: I = I₀ cos² φ
- Brewster’s angle: tan θB = n₂/n₁
- LCDs and polarized sunglasses are applications of polarization
Points to Note (Easily Confused)
① Longitudinal waves do not become polarized (it is a property only of transverse waves). ② In Malus’s law, φ is “the angle between the polarizing axis of the polarizer and the incident polarization” (the angle between the polarizers). At φ = 0, transmission is complete; at φ = 90°, extinction occurs. ③ The formula for Brewster’s angle uses tan θB (not sin or cos). ④ When unpolarized light passes through a polarizer, its intensity becomes half (because all directions are averaged).
Practice
- Polarized light passes through a polarizer. When the angle between their axes is φ = 60°, what fraction of the original intensity is transmitted?
- Find Brewster’s angle for light traveling from air (n₁ = 1.0) into glass (n₂ = 1.73) (tan 60° = 1.73).
- Explain why polarization is “evidence that light is a transverse wave,” comparing it with longitudinal waves.