Light behaves as both a particle and a wave, exhibiting properties like wavelength, frequency, and speed. These characteristics explain how light interacts with objects, leading to phenomena such as reflection, refraction, diffraction, and interference.

Understanding light's wave nature is crucial for grasping its behavior in different media. The index of refraction, which relates light's speed in vacuum to its speed in a medium, helps explain how light bends and changes wavelength when moving between materials.

Wave Behavior of Light

Wave properties of light

• Light exhibits wave-like properties characterized by wavelength ($\lambda$), frequency ($f$), speed ($v$), and wave amplitude
• Wavelength, frequency, and speed are related by the equation $v = \lambda f$
• Speed of light varies in different media
  • In vacuum, speed of light is $c = 3 \times 10^8$ m/s
  • In other media, speed of light is $v = c/n$, where $n$ is the index of refraction (water, glass)
• Wavelength changes in different media while frequency remains constant
  • Wavelength in a medium is given by $\lambda_n = \lambda_0 / n$, where $\lambda_0$ is the wavelength in vacuum

Light interactions with objects

• Ray behavior (geometric optics) occurs when object size is much larger than the wavelength of light
  • Light travels in straight lines (rays) and explains reflection and refraction (mirrors, lenses)
• Wave behavior (physical optics) occurs when object size is comparable to or smaller than the wavelength of light
  • Diffraction is the bending of light around edges or through small openings
    • Single-slit diffraction pattern consists of alternating bright and dark fringes
    • Double-slit diffraction pattern creates an interference pattern with bright and dark fringes
  • Interference is the superposition of waves
    • Constructive interference occurs when waves are in phase, resulting in bright fringes
    • Destructive interference occurs when waves are out of phase, resulting in dark fringes

Wave characteristics and interference

• Phase refers to the position of a wave in its cycle, affecting interference patterns
• Coherence is the degree of correlation between waves, essential for producing stable interference patterns
• Polarization describes the orientation of light waves' oscillations
• Young's double-slit experiment, conducted by Thomas Young, demonstrates light's wave nature through interference

Interaction of Light with Matter

Index of refraction calculations

• Index of refraction ($n$) is the ratio of the speed of light in vacuum to the speed of light in a medium, given by $n = c / v$
• Wavelength in a medium is calculated using $\lambda_n = \lambda_0 / n$
  • Wavelength decreases when light enters a medium with a higher index of refraction (water to glass)
• Speed of light in a medium is calculated using $v = c / n$
  • Speed decreases when light enters a medium with a higher index of refraction (air to water)
• Snell's law relates the angles of incidence ($\theta_1$) and refraction ($\theta_2$) at the boundary between two media: $n_1 \sin \theta_1 = n_2 \sin \theta_2$
  • Used to calculate the angle of refraction when light passes from one medium to another (air to water, glass to air)