Physics II

1
Physics II

• Lenses

2
The Grand Dichotomy

• Geometrical Optics
• The Approximation
• All rays travel in straight lines within a
  homogeneous, isotropic translucent medium
• At interfaces light behavior is exactly described
  by the law of reflection and the law of
  refraction
• No wave properties manifested
• Physical Optics
• Allow wave properties
• Diffraction, interference, etc.

3
Lenses

• Hecht A lens is a refracting device (or
  discontinuity in the transmitting media) that
  reconfigures an incoming energy distribution
• Reshapes the wave fronts by introducing time
  delays and hence phase shifts
• Hecht One wavefront is transformed into another
  provided the paths along which the energy
  propagates are all equivalent, thereby
  maintaining the phase of te wavfront.

4
Aspherical surfaces

• Parabolic, elliptical, hyperboloidal
• Consider only hyperboloidal surface in Hecht
• Transforms a diverging spherical wavefront into a
  plane wavefront.

5
Focus-directrix property

• R a/c gt 1

6
Why?

• Why does the author bring this up?
• Wants to show that spherical surfaces only
  possess focusing property approximately.
• But spheres cheaper to construct.

7
Spherical refracting surfaces

• Paraxial rays
• Rays close to axis (line of symmetry) of lens
• Angles small enough to apply small angle
  approximation
• Tan x sin x x (rad)
• 2nd principal focus
• Point at which parallal paraxial rays converge
• 1st principal focus
• Source point from which spherical waves originate
  and are refracted parallel to axis.
• Focal plane
• Plane perpendicular to axis passing through focal
  point

8
Spherical lenses

• Focal length
• For thin lens, the distance from the lens center
  to both the foci.
• Lens power
• P 1 / f
• Measured in Diopters if f is in meters
• Radius of curvature
• Radius of spherical cap of sphere comprising
  refracting surface

9
Image characteristics

• Reallight actually passes through and forms
  image
• Virtual-light only appears to come from image
  (due to belief in rectilinear propagation
• Enlarged vs. Reduced (obvious)
• Erect or Inverted (compared to source object)

10
Formulae

• Gauss thin lens equation
• 1/ so 1/ si 1/ f P
• 1 / f P (nl ns)(1 / R1 1/ R2)
• s quantities measure from center of lens.
• Follow sign conventions slavishly!!!!
• MT yi / yo - si / so .
• Newton thin lens equation
• (xo) ( xi) f2 .
• X quantities measured from focal points

11
Lens simulation web site

• http//webphysics.davidson.edu/Applets/optics4/def
  ault.html