Light and Matter: Wave-Particle Duality and the de Broglie Relation

Properties of Light Waves and Photons

• Light waves are described by their amplitude, frequency ($<br>u$), and wavelength ($ext{lambda}$ or $<br>u$).

• Light also exhibits a particle nature, composed of discrete particles called photons.

• Photons are fundamental particles of light, and evidence supporting their particle nature, such as their momentum, will be explored.

Understanding Interference

• Definition: Interference occurs when two or more waves overlap, resulting in a new wave pattern.

• Constructive Interference: Occurs when two waves of the same frequency are in phase (peaks align with peaks, troughs align with troughs). The amplitudes add up, resulting in a brighter or more intense wave.

  • Consequence: If two light waves constructively interfere, the observer perceives a brighter or more intense light.

• Destructive Interference: Occurs when two waves of the same frequency are exactly out of phase ($ext{pi}$ out of phase), meaning the peak of one wave aligns with the trough of another. The waves cancel each other out.

  • Consequence: If two light waves constructively interfere with the same amplitude, the observer perceives complete darkness (no light).

• Everyday Examples of Interference:

  • Oil Films on Water: The iridescent colors seen on oil films (e.g., after rain) are due to interference. Light reflects off both the air-oil interface and the oil-water interface. The slight difference in distance traveled by these two reflected light paths, combined with the varying thickness of the oil layer and viewing angle, causes different wavelengths (colors) of light to experience either constructive or destructive interference. This selective reinforcement or cancellation produces the observed colors.

  • Compact Discs (CDs): Holding a CD up to light reveals a rainbow spectrum. The colors are not inherent to the CD material but arise from the interference of light reflecting off the microscopic irregularities (pits and lands) on the CD surface, which act as a diffraction grating.

Wave Properties of Light

• Wavelength ($ext{lambda}$): The distance between two consecutive peaks or troughs of a wave.

• Propagation Velocity (Speed of Light, $c$): In a vacuum, the speed of light is approximately $3 imes 10^8 ext{ m/s}$.

• Frequency ($u$): The number of oscillations of the field per unit time as it passes a point of measurement.

• Relationship between wavelength, frequency, and speed of light: $<br>u = rac{c}{ ext{lambda}}$ (Frequency equals the speed of light divided by its wavelength).

Particle Nature of Light (Photons)

• Light, composed of photons, also possesses momentum.

• Experimental Evidence: Lasers can be used to slow down atoms to a complete standstill by