Light - Reflection and Refraction

• Reflection of light

  When a light ray strikes a smooth polished surface like a mirror, it bounces back
• Mirror


  An opaque object with a shiny reflective surface, which allows us to see our images
• Refraction of light

  When a light ray passes from one medium to another, its traveling speed changes, resulting in a change of direction
• Example of refraction


  • A straw in a glass appears to be bent
• Lens


  A transparent object, usually made of glass, used in eyeglasses
• Plane mirror

  • Creates virtual images that appear to be located behind the mirror at the same distance as the object in front of the mirror
  • The images are not real and cannot be projected onto a screen
  • The size of the image is the same as the size of the object
  • The images are laterally reversed (left-right reversed)
• Spherical mirror

  • A curved mirror that forms part of a sphere
  • Two types: convex mirror (outward curved reflective surface) and concave mirror (inward curved reflective surface)
• Pole


  The center point of the reflecting surface of a spherical mirror
• Center of curvature


  The center of the imaginary sphere from which the spherical mirror is derived
• Radius of curvature


  The radius of the imaginary sphere of which the mirror is a part
• Principal axis


  The line joining the pole and the center of curvature
• Principal focus


  The point where parallel rays to the principal axis meet after reflection (for concave mirrors) or appear to come from (for convex mirrors)
• Focal length


  The distance between the pole and the principal focus of a spherical mirror
• Image formation by a concave mirror

  • If the object is at infinity, the image is at the focus, highly diminished and real/inverted
  • If the object is beyond the center of curvature, the image is between the focus and center of curvature, diminished and real/inverted
  • If the object is at the center of curvature, the image is at the center of curvature, same size and real/inverted
  • If the object is between the center of curvature and the focus, the image is beyond the center of curvature, enlarged and real/inverted
  • If the object is at the focus, the image is at infinity, highly enlarged and real/inverted
  • If the object is between the pole and the focus, the image is behind the mirror, enlarged and virtual/erect
• Uses of concave mirrors

  • Shaving mirrors
  • Dentist mirrors
  • Reflectors in torchlights and vehicle lights
• Image formation by a convex mirror

  • If the object is at infinity, the image is at the focus, highly diminished and virtual/erect
  • If the object is between infinity and the pole, the image is between the pole and the focus, diminished and virtual/erect
• Uses of convex mirrors


  • Rear view mirrors in vehicles
• Sign convention for spherical mirrors

  • Distances measured to the right of the origin along the positive x-axis are positive, those to the left are negative
  • Distances measured perpendicular to and above the principal axis along the positive y-axis are positive, those below are negative
• Mirror formula

  1/v + 1/u = 1/f, where v is the image distance, u is the object distance, and f is the focal length
• Magnification


  The ratio of the height of the image to the height of the object, or the ratio of the image distance to the object distance
• Refraction of light

  The change in the direction of light passing obliquely from one medium to another, due to a change in the speed of light
• Magnification (M)


  Comparison of the size of the image with respect to the size of the object, given by M = h'/h where h' is the height of the image and h is the height of the object
• Magnification can also be found by comparing the image distance and object distance, given by M = v/u where v is the image distance and u is the object distance
• Refraction occurs when light enters from a medium with higher speed (e.g. air) to a medium with lower speed (e.g. water), causing the light ray to bend towards the normal
• Everyday phenomena due to refraction

  • Pencil appearing displaced when partly immersed in water
  • Lemon appearing bigger when kept in water in a glass tumbler
  • Letters appearing raised when seen through a glass lab
• Refraction through a rectangular glass lab

  1. Light ray bends towards the normal when entering the glass

  2. Light ray bends away from the normal when exiting the glass

  3. Angle of incidence at air-glass interface = Angle of emergence at glass-air interface
• Laws of refraction


  • The incident ray, refracted ray and the normal to the interface lie in the same plane
  • The ratio of sine of angle of incidence to sine of angle of refraction is a constant for the given pair of media (Snell's law)
• Refractive index


  A measure of how much the speed of light is reduced when passing through a medium compared to its speed in vacuum
• Refractive index is a dimensionless quantity, and a higher refractive index indicates a slower speed of light in that medium
• Absolute refractive index


  The refractive index of a medium with respect to vacuum or air
• Refractive index values


  • Water: ~1.33
  • Diamond: ~2.42
• Convex lens


  A transparent material with curved surfaces that is thicker at the center and thinner at the edges, designed to converge or focus parallel incident light rays
• Concave lens


  A transparent material with curved surfaces that curve inward, thinner at the center and thicker at the edges, designed to cause parallel incident light rays to diverge away from the virtual focal point
• Lens components


  • Center of curvature
  • Principal axis
  • Optical center
  • Aperture
  • Principal focus
  • Focal length
• Ray diagram rules for spherical lenses

  1. Ray parallel to principal axis passes through principal focus (convex) or appears to come from principal focus (concave)

  2. Ray passing through optical center emerges undeviated

  3. Rays converge at focus (convex) or diverge from virtual focus (concave)
• Image formation by convex lens

  • Object at infinity: Real, inverted, diminished image at focus
  • Object beyond 2F1: Real, inverted, diminished image between F2 and 2F2
  • Object at 2F1: Real, inverted, same-sized image at 2F2
  • Object between F1 and 2F1: Real, inverted, enlarged image beyond 2F2
  • Object at F1: Real, inverted, infinitely large image at infinity
  • Object between F1 and O: Virtual, erect, enlarged image on same side
• Image formation by concave lens

  • Object at infinity: Virtual, erect, diminished image at F1
  • Object between infinity and O: Virtual, erect, diminished image between F1 and O
• Sign convention for spherical lenses


  Same as for spherical mirrors, with all measurements taken from the optical center of the lens
• Lens formula


  1/v - 1/u = 1/f, where v is image distance, u is object distance, and f is focal length
• Magnification (M)


  M = h'/h = v/u, where h' is image height, h is object height, v is image distance, and u is object distance