Mirrors and Lenses

1
Mirrors and Lenses
2
Curved Mirror
Light Rays
Axis of symmetry
C
F

• Parallel light rays reflect off of a curved
  mirror and converge at a Focal Point
• C is the Center of Curvature for the curved
  mirror
• F is the Focal Point for incoming parallel light

3
Review Snells Law
normal
GLASS
AIR

• The change in direction is described by Snells
  Law.
• This change is dependent upon the index of the
  material (optical density) and is relative to the
  normal line.

4
Snells Law
?1
n1
n2
?2

• Snells Law n1sin?1 n2sin?2

(Or, if ?1 and ?2 are small, n1?1 n2?2)
5
Refraction for Different Materials
light
45?
AIR
WATER
GLASS
DIAMOND
32?
28?
16?
6
Flat to Curved (transmissive) Surface
A curved surface can be approximated with small
straight segments.
7
Graphical Ray Tracing
Image side ()
Source side(-)
Light Rays
Axis of symmetry
Lens

• A way to analyze optical systems.
• Modern ray tracing is often done on a computer
• Light rays always travel from left to right for
  analysis purposes.

8
Curved Interface
n
n
n
n

• Concave interface diverges rays.

• Convex interface converges rays.

Assuming n gt n
9
Convex Lens
Types
Plano-Convex
In real life
shorthand
Positive Meniscus
Double Convex
10
Convex Lens
Image side
Object side
Light Rays
Axis of symmetry
F
F
Lens

• Image focal point, F, is half the distance to
  the effective center of curvature of the lens.
• Object focal point, F, is exactly the same
  distance on the object side of the lens.

11
Convex Lens
f
f
F
F

• Image focal length, f, is the distance from the
  lens to the image focal point.
• Object focal length, f, is the distance from the
  lens to the object focal point.

12
Ray Diagrams for a Positive (Convex) Lens
Object Location
Image Type and Location
??(infinity)
Real, at F
Real, at 2F
2F
Real, at ??(infinity)
F
Virtual
lt F
13
Real vs. Virtual Images

• Real Image Image formed where light rays
  actually converge and pass through a specific
  point. Real images can be projected onto paper
  or a screen.
• Virtual Image Image formed where light rays
  appear to diverge from. Virtual images cannot be
  projected onto paper or a screen.

14
Concave Lens
Types
In real life
shorthand
Plano- concave
Negative meniscus
Double concave
15
Concave Lens
f
Light Rays
Axis of symmetry
F
Lens

• Image focal point, F, is on the object side
• Focal length, f, is negative.

16
Ray Diagrams for a Negative (Concave) Lens
Object Location
Image Type and Location
Rays converging toward F
Virtual, at ??(infinity)
Virtual, at F
??(infinity)
Virtual, between F and the lens
Approaching the lens from ??(infinity)
17
Aberrations

• Spherical lenses and mirrors, even if ground and
  polished perfectly, do not produce perfect
  images.
• The deviation in the image is called an
  aberration.

18
Chromatic Aberration

• Dispersion results in a lens having different
  focal points for different wavelengths - this
  effect is called chromatic aberration.
• Results in a halo of colors.
• Solution Use 2 lenses of different shape and
  material (achromatic doublet).

White light
FRed
FBlue
Object (small dot)
Image with chromatic aberration
.
19
Spherical Aberration

• All the rays do not bend toward the focal point,
  resulting in a blurred spot.
• Solution use lenses with aspherical curvature,
  or use a compound lens.

F
Object (small dot)
Image with spherical aberration
.
20
Other Aberrations

• Coma
• Off axis blur which looks like the coma of a
  comet.
• Astigmatism
• Different focal lengths for different planes.
• Distortion
• Images formed out of shape.

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