optics

• Optics


  • Reflection
  • Diffuse reflection
  • Refraction
  • Index of refraction
  • Speed of light
  • Snell's law
  • Geometry problems
  • Critical angle
  • Total internal reflection
  • Brewster angle
  • Fiber optics
  • Mirages
  • Dispersion
  • Prisms
  • Rainbows
  • Plane mirrors
  • Spherical aberration
  • Concave and convex mirrors
  • Focal length & radius of curvature
  • Mirror / lens equation
  • Convex and concave lenses
  • Human eye
  • Chromatic aberration
  • Telescopes
  • Huygens' principle
  • Diffraction

  
• Light


  EM wave that travels transversely (up and down motion)
• Primary colors


  • Red
  • Green
  • Blue
• White light is made up of all colors
• Black is the absence of color

  
• We see colors because objects reflect light
• If you see a color, that specific color is being reflected while the rest are being absorbed (taken in) by the medium

  
• White reflects all colors
• Black absorbs all colors

  
• Incident ray


  A ray of light heading towards an object

  
• Reflected ray


  A ray of light that reflects off an object

  
• Normal


  A perpendicular line drawn at any point on a surface
• Angle of incidence


  The angle between the incident ray and the normal

  
• Angle of reflection


  The angle between the reflected ray and the normal

  
• The law of reflection states that the angle of incidence is always equal to the angle of reflection

  
• Law of reflection


  • The incident ray, the reflected ray, and the normal to the surface all lie in the same plane
  • The angle of reflection θr equals the angle of incidence θi

  
• Diffuse reflection


  Light bounces off a non-smooth surface, with each ray still obeying the law of reflection but being reflected in many different directions

  
• Refraction


  When a wave crosses a boundary between two media, the wave changes direction (bends) because it changes velocity
• Frequency remains constant during refraction
• Velocity changes as a result of wavelength change during refraction
• Speed of light


  About 3x10^8 m/s in a vacuum, but slowed down by the presence of matter
• Light travels at about 3/4 of its vacuum speed (0.75 c) in water and about 2/3 its vacuum speed (0.67 c) in glass
• The reason for the slowing of light is because when light strikes an atom it must interact with its electron cloud
• Refraction


  A changing of direction of light at the interface between two media with different speeds

  
• Index of refraction, n

  The ratio of the speed of light in a vacuum to the speed of light in that substance
• Index of refraction values

  • Vacuum: 1
  • Air (STP): 1.00029
  • Water (20°C): 1.33
  • Ethanol: 1.36
  • Glass: ~1.5
  • Diamond: 2.42
• Snell's law


  The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant
• Snell's law


  ni sin(i) = nr sin(r)
• Willebrord Snell discovered Snell's law
• If light speeds up upon entering a new medium

  The angle of refraction, r, will be greater than the angle of incidence

  
• If light slows down in the new medium

  The angle of refraction, r, will be less than the angle of incidence

  
• Critical angle


  The incident angle that causes the refracted ray to skim right along the boundary of a substance

  
• Calculating critical angle


  c = sin^-1(nr/ni)
• Total internal reflection


  Occurs when light attempts to pass from a more optically dense medium to a less optically dense medium at an angle greater than the critical angle, resulting in no refraction, only reflection

  
• Total internal reflection can be used for practical applications like fiber optics

  
• Mirage


  Caused by the refracting properties of a non-uniform atmosphere

  
• Mirage examples


  • Seeing "puddles" ahead on a hot highway or in a desert
  • Lingering daylight after the sun is below the horizon
• Inferior mirage


  Caused by cool air being above hot air, resulting in light rays bending and reflecting to create an inverted image of the sky

  
• Dispersion


  The separation of light into a spectrum by refraction, due to the index of refraction being a function of wavelength

  
• Red light refracts less than violet light