C6 Light and Optics

• Refraction of light:

  • Direction and speed of light change when crossing the boundary between two materials with different densities
  • Example: light going from air to a glass block
  • Refraction involves changes in speed and direction of light
• Diagram of light ray passing through a glass block:

  • Incident ray: from point A to point O (same medium)
  • Refracted ray: from point O to point B (different medium)
  • Normal line (ON) must be perpendicular to the boundary
• Definition of incident angle and angle of refraction:

  • Incident angle (i): angle between incident ray and normal line
  • Angle of refraction (r): angle between refracted ray and normal line
  • Incident angle is always greater than angle of refraction
• Light ray traveling from less dense to denser medium:

  • Bends away from the normal
  • Incident angle is greater than angle of refraction
• Light ray traveling from denser to less dense medium:

  • Bends towards the normal
  • Angle of refraction is greater than incident angle
• Law of refraction:

  • Incident ray, refracted ray, and normal line all meet at the same point
  • Snell's Law: n = sin(i) / sin(r)
  • Incident angle (i) must be in vacuum for calculations
• Characteristics of refractive index:

  • Refractive index (n) is higher for denser mediums
  • Must be equal to or greater than 1
  • Has no unit
• Calculation of refractive index:

  • Example: Calculate refractive index of liquid X using Snell's Law
  • Formula: n = sin(i) / sin(r)
  • Answer should be a constant number without units
• Drawing light ray diagrams:

  • Show direction of light when traveling from less dense to denser medium
  • Label incident and refracted angles
• Reversing calculations for refractive index:

  • If calculated value is less than 1, reverse incident and refracted angles
  • Recalculate using Snell's Law to get a value greater than 1
• Experiment to determine refractive index of glass:

  • Describe the direction of light when traveling from air to glass
  • State relationship between incident and refracted angles
  • Sketch a graph and name the gradient value
  • Deduce Snell's Law based on the graph
• The relationship between the angle of incident and the angle of refraction is described by Snell's Law
• The refractive index is a value that indicates how much the speed of light is reduced when it passes through a medium
• The relationship between the incident angle and the refracted angle is found to be directly proportional
• In a scenario where light passes from a less dense medium to a denser medium, the light ray bends towards the normal line
• To find the refractive index (n), use the formula n = real depth / apparent depth
• Real depth is the depth of the object in the water
• Apparent depth is how deep the object appears to be due to refraction
• When light travels from a denser medium (water) to a less dense medium (air), it bends away from the normal
• The virtual image of an object appears above the actual object when viewed from above the water surface
• In an experiment to investigate the relationship between real depth and apparent depth, the hypothesis is that apparent depth increases as real depth increases
• Explanation for shorter appearance in water:

  • Light ray refracts away from normal line, creating a shallower image
• Explanation for shooting failure:

  • Light refracts away from normal, creating a shallower image of the fish
• Methods to hit the fish:

  • Aim slightly lower or perpendicular to the fish to hit the actual object
• Applications of light refraction:

  • Eyeglasses, magnifying glass, binoculars, camera, telescope, and microscope utilize light refraction
• Total Internal Refraction

  Critical angle: angle of incidence in optically more dense medium which angle of refraction in optically less dense medium is 90 ⁰.
• Relationship between critical angle, c and refractive index, n for a medium is n = 1/sin(θ)
• i = 0

  • no bending
  • no refraction
• i < c, where c is critical angle

  • reflect away from normal
  • refraction less than 90⁰
  • weak reflected ray
  • angle of incidence same as angle of reflection
• i = c

  • reflect away from normal
  • refraction equal to 90⁰
  • strong reflected ray
  • angle of incidence same as angle of reflection
• i > c

  • reflects internally in the glass block
  • no refraction
  • total internal reflection
  • angle of incidence = angle of reflection
• Total Internal Reflection

  • more dense to less dense medium
  • angle of incidence more than critical angle
  • i = r
  • all incident light reflected within denser medium
  • all ray and point of incidence lie in the same plane and meet at the same point
• Mirage: a natural phenomenon in which light rays produce a displaced image of distant objects through refraction and total internal reflection.
• Mirage is caused by:

  • layers of air at different heights
  • different temperatures and optical densities
  • the higher the layer of air, the colder and more optically dense the layer of air
• Rainbow is caused by:

  • water droplet is refracted and dispersed into seven different colours when light from Sun enters water droplet
  • experience total internal reflection within water droplet
  • seven colours are refracted and dispersed again when emerging from water droplet to air
• Convex lens

  • converging lense
  • focal point is real
  • focal length is positive
• Concave lens

  • diverging lense
  • focal point is virtual
  • focal length is negative
• Convex Lens

  Object at infinity (RID) ; Real, Inverted, Diminished

  Object beyond 2F (RID) ; Real, Inverted, Diminished

  Object at 2F (RIS) ; Real, Inverted, Same size

  Object between F and 2F (RIM) ; Real, Inverted, Magnified

  Object at F (VUM) ; Virtual, Upright, Magnified

  Object between F and optical centre (VUM) ; Virtual, Upright, Magnified
• Concave lens

  Object beyond optical centre (VUD) ; Virtual, Upright, Diminished
• Linear Magnification, m

  = Image height, hi / Object height, ho

  = Image distance, v / object distance, u