Transcript Physics 214 1: Geometric Optics Huygens Principle Diffraction

Physics 214
1: Geometric Optics
•Huygens Principle
•Diffraction
•Reflection
•specular
•diffuse
•Refraction
•Snells Law
•Index of Refraction
•Dispersion
•Mirrors
•
•
•
•
•
•
Images formed by refraction
Lens Makers Equation
Thin lenses
Combination of thin lenses
Aberration
Optical Instruments
Huygens Principle
wavelets
wavefront
•Geometric Approximation
•Direction of rays = direction of energy
flow
•Rays are straight lines perpendicular
to wavefronts
l = wavelength
d =width of opening
l  d cannot approximate as point source
l << d no change in direction of light rays
l >>d change in direction of light rays
 DIFFRACTION
sharp shadows are cast when NO diffraction
occurs
Reflection
specular
diffuse
reflected wave
angle
of
reflection
angle
of
incidence
incident
wave
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
virtual
image
Spherical Mirrors
•curved mirrors, whose reflecting surfaces are
sections of spheres.
Concave Mirror
C F
paraxial
rays
center of
curvature
principal
axis
Focal point - real
Convex Mirror
C
F
Virtual Focal Point
Type of Mirro r
Object Distance as
Compared to Focal
Length
Characteristics of Image
Concave
d > 2f
real, inverted, diminished
d = 2f
real, inverted, same size
f < d < 2f
real, inverted, magnified
d<f
virtual,erect,magnified
Convex
for any d
virtual, erect, diminished
Mirror Equations
1
do
m
+
=
1
di
hi
ho
=
1
f
=
- di
do
2
r
=
=
lateral magnification
•distances on reflecting side of mirror are positive
•object & image height is positive above (direct
image) principal axis, negative (inverted image)
below.
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.
Refraction
reflected
angle
of
refraction
angle
of
incidence
incident
refracted
•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
Snells Law:
sin q 2
v2
=
= constant
sin q 1
v1
c
Index of Refraction
n=
v
 n1 sin q 1 = n 2 sin q 2
n 1 = index of refraction of first material
n 2 = index of refraction of second material
q 1 = angle of incidence
q 2 = angle of refraction
Light travelling from one medium to another has
CONSTANT FREQUENCY
v = ln
\v1 = l1n and v2 = l2n
l1 v1 n1
 =
=
l 2 v2 n2
If medium 1 is air or a vacuum
l0
n(l) =
l
DISPERSION
Continuous Spectra
reflected
angle
of
incidence
angle
of
refraction
(b)
incident
(a)
refracted
transmitted
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
n2
n2
0
sinq c =
sin 90 =
n1
n1
Images formed by Refraction
q1
R q2
s
for q 1 and q 2 small
s’
(paraxial rays)
n1
n2
n 2 - n1
+
=
s
s
R
Real Object
s positive
in front of
surface
Virtual
Object
s negative
behind
surface
Real Image
s' positive
behind
surface
Virtual Image
s' negative
in front of
surface
Real center
of curvature
R positive
behind
surface
Virtual center
of curvature
R negative
in front of
surface
For plane surfaces
n1
n2
n2
=
 s  = s ( virtual image)
s
s 
n1
n2
 relative index of refraction
n1
Thin Lenses
•Image formed by one refracting surface is
•Object of second surface
The focal length of a lens is defined as
the image distance
S'
when the object is
at , i.e. f = swhen s= .
1 1 
1 1 1
 = + = (n- 1) - 
R1 R2 
f s s
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
Lenses
Double
Convex
Plano
Convex
Convex
meniscus
Double
Concave
Plano
Concave
Concave
Meniscus
Ty pe of Le n s
Conv e x
Object Distance as
Compared to Focal
Length
d > 2f
real, inverted, diminished
d = 2f
real, inverted, same size
f < d < 2f
real, inverted, magnified
d=f
d<f
Concave
Characteristics of Image
for any d
no image formed
v i r t u a l ,er e ct ,m a g ni f i e d
v i r t ua l , er ect , d i m i ni sh ed
•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.
1
o
F I
2
•Ray 1 (appears to) come from focal point
•Ray 2 passes through center of lens
Combination of thin lenses
1 1
1
1
+
=
+
f2
s s  f 1
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
f1
f2
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
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
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 fnumber equals the ratio of the focal length to the
lens diameter
1
f
I
f - number
=
2 ;
f
D
D
( )
•Eye
•The power of a lens in Diopters is the reciprocal of the
focal length measured in meters (including sign)
1
p =
f
•Simple Magnifier
•When an object is at the near point of the eye ( 25 cm)
the angle subtended by the object is qWhen a
convex lens of focal length f is placed between the
eye and the object an image which subtends an
angle q0 can be formed at the near point
angular magnification
q
m =
= 1 +
q0
25
f
•Compound Microscope
L 
 25 

M = f0  f e 
•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
•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
m = -
f0
fe