Reflection, Refraction and Lenses

• Reflection

  • Reflection is the change in direction of a wavefront at an interface between media, returning it to its origin.
  • The law of reflection says the angle of incidence equals the angle of reflection.
  • The incident ray, reflected ray, and normal are all in the same plane.

• Refraction

  • Refraction is the change in a wave's direction as it passes between media due to speed change.
  • Snell's Law relates incidence and refraction angles for waves through isotropic media like water, glass, or air.
  • Snell's Law states the ratio of the sines of incidence and refraction angles equals the ratio of velocities or refractive indices.
  • Refractive index is the ratio of light speed in a vacuum to its speed in a medium.

Lenses

• A lens is a transmissive optical device that focuses or disperses a light beam by refraction.
• Lenses are in optical instruments, from magnifying glasses to cameras.
• Lenses are converging (convex) or diverging (concave).
  • Converging lenses focus parallel light rays.
  • Diverging lenses spread parallel light rays.
• Focal length is the distance from the lens to where parallel rays converge (converging lenses) or appear to diverge (diverging lenses).
• The lensmaker's equation links focal length to refractive index and surface curvature radii.
• The thin lens equation relates object distance, image distance, and focal length: 1/f = 1/do + 1/di

Mirrors

• A mirror is a surface that reflects a clear image.
• Mirrors can be plane (flat) or curved.
• Curved mirrors are concave (converging) or convex (diverging).
• The focal length of a curved mirror is half the radius of curvature.
• The mirror equation: 1/f = 1/do + 1/di
• Magnification (M) = -di/do

Total Internal Reflection

• Total internal reflection (TIR) occurs when a wave hits an interface at an angle greater than the critical angle.
• Above the critical angle, the wave is entirely reflected.
• TIR happens when light goes from a higher to a lower refractive index medium.
• The critical angle is where the refraction angle is 90 degrees.
• sin(θc) = n2/n1, where θc is the critical angle.
• n1 is the refractive index of the origin medium, and n2 is the refractive index of the destination medium.
• Applications include optical fibers, prisms, and sensors.

Wave Optics

• Wave optics studies interference, diffraction, polarization, where geometric optics fails.
• Wave optics treats light as an electromagnetic wave.

Young's Double-Slit Experiment

• Young's experiment shows the wave nature of light.
• Light through two slits creates an interference pattern on a screen.
• The pattern has alternating bright and dark fringes.
• Bright fringes (constructive interference): path difference is a multiple of the wavelength.
• Dark fringes (destructive interference): path difference is an odd multiple of half the wavelength.
• Bright fringe position: dsin(θ) = mλ (d = slit separation, θ = angle, m = fringe order, λ = wavelength).
• Dark fringe position: dsin(θ) = (m + 1/2)λ.

Interference

• Interference occurs when two or more waves overlap.
• Constructive interference: waves are in phase, amplitude increases.
• Destructive interference: waves are out of phase, amplitude decreases.
• Constructive interference condition: path difference is a multiple of the wavelength.
• Destructive interference condition: path difference is an odd multiple of half the wavelength.
• Interference works for light, sound, water, etc.

Diffraction

• Diffraction is the bending of waves around obstacles or through openings.
• Diffraction is significant when obstacle/opening size is comparable to the wavelength.
• Single-slit diffraction creates a pattern with a central bright fringe and dimmer fringes.
• Dark fringe positions: asin(θ) = mλ (a = slit width, θ = angle, m = fringe order, λ = wavelength).
• Diffraction gratings split light into beams traveling in different directions.
• Beam directions depend on grating spacing and wavelength.
• Diffraction gratings are used in spectrometers.