Index of Refraction
In general, the speed of light in any material is less that its speed
in vacuum.
Index of refraction of a medium is defined in terms of the
speed of light in this medium
c
n
v
v1 T = 1 , v2 T = 2
Hence
1
2
1 v1 n 2


 2 v 2 n1
reflection and refraction
The law of reflection:
angle of
incidence
incident
ray
angle of
reflection
1
’1
reflected
ray
The reflected ray lies in the
plane of incidence and the
angle of reflection ’1 is equal
to the angle of incidence ’
’1 = 1
The law of refraction:
2
refracted
ray
angle of
refraction
The refracted ray lies in
plane of incidence and
angle of refraction 2
related to the angle
incidence 1 by
n1 sin 1 = n2 sin 2
the
the
is
of
the law of reflection
and the law of refraction
A’
AB v 2 n1


A ' C v1 n 2
D
1
’1
A 
2
C
AB  AC  sin 2
A' C  AC  sin 1
B
A' C  AD
sin 1 
A' C AD

AC AC
1  '1
 sin '1
sin 2 n1

sin 1 n 2
n 2 sin 2  n 2 sin 1
Prism and Dispersion
Index of refraction of a material is
a function of the wavelength
60

50
deviatio
n angle
angle
dispersi
on angle




seeing objects
In order to be seen, an
object must send light from each
of its points in many directions.
The eye collects some of the light
emitted from a point allowing the
brain to interpret the location of
the point.
In some situations diverging rays are interpreted as
originating from a single point creating an image of a point.
plane mirror
If the rays are emitted from a point (real object) or converge to a
point (virtual object), after they are reflected by the mirror, the
rays or their extensions meet at a point to form an image.
reflecting
surface
object
(real)
s
image
(virtual)
s’
image
(real)
s
object
(virtual)
s’
spherical mirror
If the rays are emitted from a point (real object) or converge to a
point (virtual object), after they are reflected by the mirror, the rays
or their extensions meet approximately at a point to form an image.
O
(object) parallel ray
(object) chief ray
(object)
normal ray
(object)
focal ray
F
principal
axis
C
(image) parallel ray
(image)
chief ray
(image)
focal ray
I
(image)
normal ray
the mirror equation:
from geometrical
considerations:
s
h
sR


s '  h ' R  s'
R
O
h
h’
C
I
sR  ss'  ss's' R
s’
s
sR  s' R  2ss'
0
1 1 2 1
  
s' s R f
For a concave mirror the focal length is positive and for a
convex mirror the focal length is negative.
thin spherical lens
If the rays are emitted from a point (real object) or converge to a
point (virtual object), after they are refracted by the lens, the rays
or their extensions meet approximately at a point to form an image.
O
(object) parallel ray
(object) chief ray
Fi
(object) focal ray
Fo
(image) parallel ray
I
(image)
focal ray
(image)
chief ray
positive object’s position
positive image position
f
O
h
Fi
h’
Fo
I
s
h
s
f


 h ' s'
s'f
fs'  s' s  fs
fs'fs  s' s
s’
thin lens equation
1 1 1
 
s s' f
lens maker's equation
R1>0
n0
n
R2<0
The focal length of a thin-lens is determined by the curvatures
of the two surfaces, the index of refraction of the lens material,
and the index of refraction of the surrounding medium
 1
1  n
1 

   1

f  n 0  R1 R 2 
Magnification
h'
s'
M  
s
h
Object
h
s
s’
Fi
Fo
h’
Image
The magnification is defined as the ratio of the image height to the
object height.
If the orientation of the image is the same as that of the object, a
positive value is assigned to the magnification.
For an inverted image the magnification is negative.
angular magnification
example: magnifying glass
N
The angular magnification
(magnifying power) of an
instrument is defined as the
ratio of the "angular size" of
the final image and the
"angular size" of the
observed object.
'
m

h
h’

’
s
N
h'
s  h  N  N
' 

N
N
N s
s
h
m
N
s
vision
retina
cornea
Fi
Fo
lens
If the object is between the near and the far point of the eye, its
lens the eye muscles adjust the focal length of the lens to form a
real image on the retina.
two thin lenses in contact
O1
s'  s 2 ' F2i
s  s1
F1o
F1i
s1 '  s2
F2o
O
I1 2
1 1 1
 
s s1 ' f1
1 1 1
 
s1 s1 ' f1
1 1
1


s2 s2 ' f2

1 1 1
 
s1 ' s' f 2
1 1 1 1
  
s s' f1 f1
The system of two close lenses behaves like a single lens with a
focusing power equal to the sum of the focusing powers of each lens
separately.
compound microscope
The objective produces the first
(real) image almost at the focal
point of the ocular.
The eye piece form the final
(virtual) image between the near
and the far point of the observer’s
eye.
angular magnification
Lh L
L2
' h ' h

 
m  
L
f of e h
fof e
 fe
eye piece
L
objective
specimen
Keplerian telescope
The objective produces the first (real) image almost at its focal
point and the focal point of the ocular.
The eye piece form the final (virtual) image between the near
and the far point of the observer’s eye.
h’
angular magnification
fo
h' h '
'

m  
fe
fe f o
