phy203_3

1
Physics 214
1 Geometric Optics

• Huygens Principle
• Diffraction
• Reflection
• specular
• diffuse
• Refraction
• Snells Law
• Index of Refraction
• Dispersion
• Mirrors

2

• Images formed by refraction
• Lens Makers Equation
• Thin lenses
• Combination of thin lenses
• Aberration
• Optical Instruments

3
Huygens Principle
wavelets
wavefront
4

• Geometric Approximation
• Direction of rays direction of energy flow
• Rays are straight lines perpendicular to
  wavefronts

5
(No Transcript)
6
Reflection
specular
diffuse
7
reflected wave
angle of reflection
angle of incidence
incident wave
8
Laws of Reflection

• Specular / Mirror Reflection
• from smooth surface
• Angle of incidence angle of reflection
• Diffuse Reflection
• from rough surface

Plane Mirrors

• Image is
• erect
• virtual
• left-right reversed

9
virtual image
10
Spherical Mirrors

• curved mirrors, whose reflecting surfaces are
  sections of spheres.

Concave Mirror
principal axis
C
F
center of curvature
paraxial rays
Focal point - real
11
Convex Mirror
C
F
Virtual Focal Point
12
T
y
p
e

o
f

M
i
r
r
o

r
Object Distance as
Characteristics of Image
Compared to Focal
Length
C
o
n
c
a
v
e
d gt 2f
real, inverted, diminished
d 2f
real, inverted, same size
f lt d lt 2f
real, inverted, magnified
d lt f
v
i
r
t
u
a
l
,
e
r
e
c
t
,
m
a
g
n
i
f
i
e
d
Convex
for any d
virtual, erect, diminished
13
Mirror Equations
1
1
1
2



d
d
f
r
o
i
h
-
d
m



i
i
h
d
o
o
lateral magnification

• distances on reflecting side of mirror are
  positive
• object image height is positive above (direct
  image) principal axis, negative (inverted
  image) below.

14
Spherical Aberration
It is only approximately true that rays that
make a small angle with the principal axis come
to a perfect focus at the focal point. Thus
images become blurred. This defect is called
spherical aberration. This defect is minimized
the smaller the mirror is compared to its focal
length.
15
Refraction
16
reflected
angle of refraction
angle of incidence
incident
refracted
17

• Speed of light is slower in denser materials
• Index of refraction is greater
• In denser medium angle of light ray to the normal
  of the surface between mediums is smaller than
  the corresponding angle in the in the less dense
  medium.
• paths of light rays are reversible

18
Snells Law
sin
q
v


constant
2
2
sin
q
v
1
1
c
Index of Refraction
n

v
Þ

n
sin
q

n
sin
q
1
1
2
2
n

index of refraction of first material
1
n

index of refraction of second material
2
q

angle of incidence
1
q

angle of refraction

2
19
(No Transcript)
20
Continuous Spectra
21
reflected
angle of incidence
angle of refraction
(b)
(a)
incident
transmitted
refracted
22
Total Internal Reflection
At a particular incident angle the angle of
refraction will be 90 degrees. The incident
angle at this point is called the critical
angle. For any incident angle greater than this
angle light will be reflected at the boundary
23
(No Transcript)
24
Images formed by Refraction
?1
R
?2
s
s
for
q
and
q
small
(
paraxial rays
)
1
2
n
n
n
-
n


1
2
2
1
s

s
R

25
(No Transcript)
26
For plane surfaces
n
n
n
1

2
Þ

s

-
2
s
(
virtual image
)
s

s
n
1
n
º
relative index of refraction
2
n

1

• Thin Lenses
• Image formed by one refracting surface is
• Object of second surface
  

27
The focal length of a lens is defined as
the image distance
S'
when the object is



at
,
i.e. f

s
when s

.
æ
ö
1
1
1
1
1
(
)
Þ



-
ç

n
-
1

R
R
è
ø
f
s
s
1
2
Lens Maker Equation
A thin lens has 2 focal points depending on
whether incident rays come from left or right.


h
s

-
Lateral magnification

m

h
s

28
Lenses
Double Convex
Plano Convex
Convex meniscus
29
Double Concave
Plano Concave
Concave Meniscus
30
(No Transcript)
31

• Focal length is positive for converging lenses
  and negative for diverging lenses.
• Object distance is positive if it is on side of
  lens that light is coming from (not always true!)
• Image distance is positive if it is on the
  opposite side of lens that light is coming from.
• Object and image heights are positive above the
  axis, negative below.

32
1
F I
o
2

• Ray 1 (appears to) come from focal point
• Ray 2 passes through center of lens

33
Combination of thin lenses
1
1
1
1



s

s
f
f
1
2
s

object distance from first lens

s

image distance from second lens
if the lenses are touching they act as
a single lens with focal length
1
1
1



f
f
f

1
2
34
Lens Aberrations
Lens and mirror equations assume ray makes small
angle with optic axis, if this is not the case,
imperfect blurred images are formed, this is
called ABERRATIONS
spherical aberration
35
chromatic aberration

• Other Aberrations
• Astigmatism
• point object off the axis produces two line
  images at different points.
• Coma
• off axis object produces a coma shaped image
• Distortion
• magnification for off axis points different than
  for on axis points

36
Optical Instruments

• Camera
• The light intensity I incident on the film per
  unit area is inversely proportional to the square
  of the ratio of the diameter of the lens to its
  focal length. The f-number equals the ratio of
  the focal length to the lens diameter

• Eye
• The power of a lens in Diopters is the reciprocal
  of the focal length measured in meters
  (including sign)

37
(No Transcript)
38

• Simple Magnifier
• When an object is at the near point of the eye (
  25 cm) the angle subtended by the object is
  ???When a convex lens of focal length f is
  placed between the eye and the object an image
  which subtends an angle ?0 can be formed at the
  near point

angular magnification
q
25
m


1

q
f

0
39

• Compound Microscope
• objective focal length of f0
• eye piece of focal length fe
• the two lenses are separated by a distance L
• For object located just beyond focal point of
  objective, the two lenses combined form an
  enlarged virtual and inverted image of lateral
  magnification M

æ
L
25
ö
ç

M

-
f
f
è
ø

0
e
40

• Astronomical telescope
• Two convex lenses are separated by a distance
  equal to the sum of their focal lengths. The
  angular magnification is equal to the ratio of
  the two focal lengths

f
0
m

-
f

e