Refraction

• Refraction is the change in the direction of light when it passes from one medium to another of different optical density
• Optical density is related to the transparency of a substance to light
• The higher the optical density of a material, the slower the light travels through it
• Index of refraction or refractive index is the ratio of the speed of light in a vacuum to that in the material
• N is the index of refraction
• c is the speed of light
• v is the speed of light in the substance
• the incident ray, the refracted ray, and the normal all lie on the same plane
• Laws of Refraction

  1. The incident ray, the refracted ray, and the normal all lie on the same plane

  2. When a ray of light passes obliquely from an optically denser medium to a less dense medium, it is refracted away from the normal

  3. When a ray of light passes obliquely from an optically less dense medium to a denser medium, it is refracted toward the normal

  4. When the incident ray is perpendicular to the interface (ie., at an angle of incidence of zero degrees), no bending of the light occurs
• Snell's law relates the indices of refraction of two media and the angles from the normal using the equation, sin(w1)/sin(w2) = n2/n1
• w1


  Angle of incidence
• w2


  Angle of refraction
• n1


  Index of refraction of the incident medium
• n2


  Index of refraction of the refractive medium
• Snell's law is named after Dutch astronomer and mathematician Willebrord Snell
• Shallowing effect


  Objects submerged in a liquid appear to be shallower than they actually are
• The index of refraction is the ratio of the real depth to the apparent depth
• Real depth


  The actual depth of the coin in water
• Apparent depth


  The depth the coin appears to be when viewed through the water
• the angle of incidence corresponding to an angle of refraction of 90 degrees is called the critical angle
• Converging lens


  When a beam of parallel rays falls on a convex lens, the rays are refracted and converge to a point called the principal focus F
• Diverging lens


  Parallel rays falling upon a concave lens spread out. When extended, the refracted rays will appear to come from a point in front of the lens, which is considered the principal focus
• Focal length

  The distance from the optical center of the lens to the principal focus
• Principal focus


  For converging lenses, the focal point behind the lens. For diverging lenses, the focal point in front of the lens
• Secondary focus


  For converging lenses, the focal point in front of the lens
• Principal axis


  The line joining the optical center and the principal focus
• Types of lenses

  • Converging
  • Diverging
• If the angle of incidence is greater than the critical angle, no refraction occurs
• When light is reflected back to the first medium, this phenomenon is called total internal reflection
• Ray diagram for image formation by a convex lens

  • Consider the ray parallel to the principal axis and the ray passing through the optical center of the lens
  • The intersection of the refracted rays gives the position of the image
• Tracing images formed by converging and diverging lenses

  1. Principal rays

  2. Refracted rays
• Convex lens images


  • The type of image formed depends on the distance of the object from the lens
  • Real if the distance is greater than the focal length
  • Virtual if the distance is less than the focal length
• Characteristics of images formed by a convex lens

  • Real, inverted, very small (almost a point) (object at infinity)
  • Real, inverted, smaller than the object (object beyond 2F)
  • Real, inverted, same size as the object (object at 2F)
  • Real, inverted, bigger than the object (object between F and 2F)
  • No image (object at secondary focus)
  • Virtual, upright, bigger than the object (object between F and lens)
• Concave lenses form the same kind of image as convex mirrors, and convex lenses form the same image as concave mirrors
• Ray diagram for image formation by a concave lens


  For any object distance from the lens, the image formed is virtual, upright, smaller than the object, and located on the same side of the lens as the object
• Thin lens equation


  • Relates object distance (d), image distance (d'), and focal length (f) of the lens
  • Focal length is positive for a converging lens and negative for a diverging lens
  • Real image distance is positive, virtual image distance is negative
• Magnification


  Size of image / Size of object
• The thin lens equation and the formula for magnification are similar to those for mirrors