25.1 The Ray Aspect of Light

Light behaves in fascinating ways, traveling through emission, absorption, transmission, reflection, and refraction. Understanding these modes helps us grasp how light interacts with different materials and environments, shaping our visual world.

Geometric optics simplifies light as rays, making it easier to predict its behavior in everyday situations. This approach allows us to explain phenomena like shadows, pinhole cameras, and the laws of reflection and refraction, which are crucial for understanding optics.

Light as a Ray

Modes of light travel

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• Emission generates light from a source (sun, light bulb, laser)
• Absorption occurs when an object absorbs light energy
  • Absorbed energy can be converted to heat or cause the object to emit light at a different wavelength
• Transmission allows light to pass through a medium without being absorbed
  • The speed of light may change based on the medium's refractive index
• Reflection causes light to bounce off a surface, changing its direction
  • The angle of incidence equals the angle of reflection
• Refraction bends light when it passes between media with different refractive indices
  • The angle of refraction depends on the refractive indices and angle of incidence, described by Snell's law: $n_1 \sin \theta_1 = n_2 \sin \theta_2$

Light behavior as rays

• Geometric optics treats light as rays traveling in straight lines when interacting with objects much larger than its wavelength
  • This approximation is valid for everyday situations (light reflecting off mirrors, refracting through lenses)
• Opaque objects blocking light rays cast shadows
  • Shadow size and shape depend on object size and shape, light source size, and distance between object and light source
• Pinhole cameras use a small aperture to focus light rays from a scene onto a screen or film
  • The image is inverted and can be used to study light behavior as rays
• Polarization of light rays can occur when light is reflected or transmitted through certain materials

Laws of reflection and refraction

1. Law of reflection states the angle of incidence equals the angle of reflection: $\theta_i = \theta_r$
   • The incident ray, reflected ray, and normal to the surface at the point of incidence lie in the same plane
2. Law of refraction (Snell's law) relates the angles of incidence and refraction to the refractive indices of two media: $\frac{\sin \theta_1}{\sin \theta_2} = \frac{n_2}{n_1}$
   • The incident ray, refracted ray, and normal to the surface at the point of incidence lie in the same plane
3. Total internal reflection occurs when light travels from a higher to lower refractive index medium above a critical angle of incidence
   • All light is reflected back into the first medium
   • The critical angle is given by: $\theta_c = \arcsin(\frac{n_2}{n_1})$, where $n_1 > n_2$
4. Dispersion separates white light into its constituent colors when refracted due to different wavelengths having slightly different refractive indices in a given medium
   • This effect is seen in prisms and rainbows (demonstrating the electromagnetic spectrum)

Wave-particle duality and interference

• Light exhibits both wave-like and particle-like properties, known as wave-particle duality
• Interference occurs when light waves interact, resulting in constructive or destructive interference patterns
• Coherence of light waves is necessary for observable interference effects