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3.1. Light
• Visible light is an example of an electromagnetic
(em) wave and consists of electric and magnetic
harmonic waves that vibrate in phase at the same
frequency but at right angles to each other .
• The electric field is given by
• E(x,t) =Eosin(kx-wt)
• and the magnetic field is given by
• B(x,t) =Bosin(kx-wt)
• E and B are related through E = cB
• With c the speed of light. Hence the electric field
is very much greater than the magnetic field and
light is usually described in terms of the E field.
3.1. Light
• The energy carried by the wave flows at right angles to
both the electric and magnetic fields. It is quantified by
the Poynting vector S.
S
ExB
o
The speed of light in a vacuum is given by.
c
1
 o o
 of the Poynting vector to determine the
We can use the idea
time averaged intensity Iav of a light source.
1

I av  ocE
2
This gives the energy flow or flux through a surface of area
of 1 m2 in 1 s.

2
The successive
planes show the
direction of
energy flow
3.2. Generation of an em wave
Maxwell showed theoretically that when a charge accelerates
the charge generates an electromagnetic wave. The moving
charge generates both an electric and magnetic field that are
at right angles to each other.
This was proved experimentally by Hertz who detected the
waves created when an inductor - capacitor (LC) circuit was
used to temporally ionize the air in the capacitor. By measuring
the output signal Hertz showed the output was an em wave.
3.3. Light rays and Geometrical Optics
• The Poynting vector allows us to determine the
direction of energy flow.
• The direction of this energy flow can be indicated
by a ray
• The rays are drawn as straight lines that are
perpendicular to the wave front.
• Geometrical optics is concerned with the study of
the behaviour of these rays at of the rays at
interfaces between different media.
Wave front
Rays
3.4. Rays and Reflections
• Consider a perfectly flat reflecting surface.
• A plane wave front AB is incident on this surface at an angle
qi. It is reflected at an angle qr to form wave front CD
N
C
N
B
qr
q
q
A
qr
D
• The lines perpendicular to the reflecting surface are called
Normals.
• All the rays and normals lie in the same plane - the plane of
incidence
3.4. Rays and Reflections
• The rays associated with the wave front AB make are
incident at an angle qi to the normal whilst those belonging
to CD make an angle qr.
N
C
N
B
qr
q
q
A
qr
D
• In the time taken for the wave front to move from B to D
the reflected ray moves from A to C. This is a consequence
of Huygens’ Principle.
3.4. Rays and Reflections
•
•
•
•
•
•
•
As the rays are in the same medium then
AC = BD
But AC = ADsinqr and
BD = ADsinqi
So qi = qr
This is the law of reflection.
Whenever a ray is reflected from a surface the angle of
incidence is always equal to the angle of reflection.
3.4. Rays and Reflections
• Whenever a ray is reflected from a surface, the angle of
incidence is always equal to the angle of reflection.
• If the surface is perfectly flat then all the rays are
reflected in the same direction -Specular reflection
• If the surface is rough, even though the rays are incident
on the surface at the same angle the rays are reflected in
different directions -Diffuse reflection
3.5. Deviation caused by reflection
• Whenever a ray is reflected from a surface, the angle of
incidence is always equal to the angle of reflection.
• The ray is deviated from its original path.
• The angle of deviation f is given by
• f = π - 2qi
incident
ray
reflected
ray
N
q q
q
f
undeviated
ray
3.6. Image formation with plane mirrors
• Consider an object that is placed a distance P from a plane
mirror. The image is formed a distance Q from the mirror.
• The image is found by projecting the reflected rays back
into the mirror. Where the rays cross the image is formed.
Here tani = H/P
and tani = H/Q
So P = Q.
Thus for a plane mirror
the image is formed as
far behind the mirror
as the object is in
front. The image is
also laterally inverted.
P
Q
i
H
i
P
i
Q
3.6. Real and virtual objects and images
• The image produced by a plane mirror is a virtual image. It
cannot be imaged onto a screen.
P
• Objects and images can be
classified by the way the rays
behave.
Q
i
H
i
P
i
Q
•A real object - Rays diverge - energy flows from object
•A real image - Rays converge - energy flows to image
•A Virtual object- Rays converge - No energy come from object
•A Virtual image - Rays diverge - No energy goes to image